Differential Equations
4th Edition
ISBN: 9780495561989
Author: Paul Blanchard, Robert L. Devaney, Glen R. Hall
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 1, Problem 29RE
In Exercises 21-29,
(a) specify if the given equation is autonomous, linear and homogeneous, linear and nonhomogeneous, and/or separable, and
(b) find its general solution.
29.
dydt=−3y+e−2t+t2
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
A side view of a recycling bin lid is diagramed below where two panels come together at a right angle.
45 in
24 in
Width? —
Given this information, how wide is the recycling bin in inches?
f'(x)
If you are using chatgpt leave it
I will downvote .
Chapter 1 Solutions
Differential Equations
Ch. 1.1 - In Exercises 1 and 2, find the equilibrium...Ch. 1.1 - In Exercises 1 and 2, find the equilibrium...Ch. 1.1 - Consider the population model dPdt=0.4P(1P230)...Ch. 1.1 - Consider the population model ...Ch. 1.1 - Consider the differential equation dydt=y3y212y...Ch. 1.1 - In Exercises 6—10, we consider the phenomenon of...Ch. 1.1 - In Exercises 6—10, we consider the phenomenon of...Ch. 1.1 - In Exercises 6—10, we consider the phenomenon of...Ch. 1.1 - In Exercises 6—10, we consider the phenomenon of...Ch. 1.1 - In Exercises 6—10, we consider the phenomenon of...
Ch. 1.1 - MacQuarie Island is a small island about half-way...Ch. 1.1 - The velocity u of a freefalling skydiver is well...Ch. 1.1 - Exercises 13—15 consider an elementary model of...Ch. 1.1 - Exercises 13—15 consider an elementary model of...Ch. 1.1 - Exercises 13—15 consider an elementary model of...Ch. 1.1 - The expenditure on education in the U.S. is given...Ch. 1.1 - Suppose a species of fish in a particular lake has...Ch. 1.1 - Suppose that the growth-rate parameter k = 0.3 and...Ch. 1.1 - The rhinoceros is now extremely rare. Suppose...Ch. 1.1 - While it is difficult to imagine a time before...Ch. 1.1 - For the following predator-prey systems, identify...Ch. 1.1 - In the following predator-prey population models,x...Ch. 1.1 - The following systems are models of the...Ch. 1.2 - Bob. Glen. and Paul are once again sitting around...Ch. 1.2 - Make up a differential equation of the form ...Ch. 1.2 - Make up a differential equation of the form dy/dt...Ch. 1.2 - In Section 1.1, we guessed solutions to the...Ch. 1.2 - In Exercises 524, find the general solution of the...Ch. 1.2 - In Exercises 524, find the general solution of the...Ch. 1.2 - In Exercises 524, find the general solution of the...Ch. 1.2 - In Exercises 524, find the general solution of the...Ch. 1.2 - In Exercises 524, find the general solution of the...Ch. 1.2 - In Exercises 524, find the general solution of the...Ch. 1.2 - In Exercises 524, find the general solution of the...Ch. 1.2 - In Exercises 524, find the general solution of the...Ch. 1.2 - In Exercises 524, find the general solution of the...Ch. 1.2 - In Exercises 524, find the general solution of the...Ch. 1.2 - In Exercises 524, find the general solution of the...Ch. 1.2 - In Exercises 524, find the general solution of the...Ch. 1.2 - In Exercises 524, find the general solution of the...Ch. 1.2 - In Exercises 524, find the general solution of the...Ch. 1.2 - In Exercises 524, find the general solution of the...Ch. 1.2 - In Exercises 524, find the general solution of the...Ch. 1.2 - In Exercises 524, find the general solution of the...Ch. 1.2 - In Exercises 524, find the general solution of the...Ch. 1.2 - In Exercises 524, find the general solution of the...Ch. 1.2 - In Exercises 524, find the general solution of the...Ch. 1.2 - In Exercises 2538, solve the given initial-value...Ch. 1.2 - In Exercises 2538, solve the given initial-value...Ch. 1.2 - In Exercises 2538, solve the given initial-value...Ch. 1.2 - In Exercises 2538, solve the given initial-value...Ch. 1.2 - In Exercises 2538, solve the given initial-value...Ch. 1.2 - In Exercises 2538, solve the given initial-value...Ch. 1.2 - In Exercises 2538, solve the given initial-value...Ch. 1.2 - Prob. 32ECh. 1.2 - Prob. 33ECh. 1.2 - In Exercises 2538, solve the given initial-value...Ch. 1.2 - In Exercises 2538, solve the given initial-value...Ch. 1.2 - In Exercises 2538, solve the given initial-value...Ch. 1.2 - In Exercises 2538, solve the given initial-value...Ch. 1.2 - Prob. 38ECh. 1.2 - A 5-gallon bucket is full of pure water. Suppose...Ch. 1.2 - Consider the following very simple model of blood...Ch. 1.2 - A cup of hot chocolate is initially 170o Fand is...Ch. 1.2 - Suppose you are having a dinner party for a large...Ch. 1.2 - Prob. 43ECh. 1.3 - In Exercises 1-6, sketch the slope fields for the...Ch. 1.3 - Prob. 2ECh. 1.3 - Prob. 3ECh. 1.3 - Prob. 4ECh. 1.3 - Prob. 5ECh. 1.3 - Prob. 6ECh. 1.3 - In Exercises 710, a differential equation and its...Ch. 1.3 - Prob. 8ECh. 1.3 - Prob. 9ECh. 1.3 - Prob. 10ECh. 1.3 - Suppose we know that the function f(t, y) is...Ch. 1.3 - Prob. 12ECh. 1.3 - Prob. 13ECh. 1.3 - Prob. 14ECh. 1.3 - Consider the autonomous differential equation ...Ch. 1.3 - Eight differential equations and four slope fields...Ch. 1.3 - Prob. 17ECh. 1.3 - Prob. 18ECh. 1.3 - Prob. 19ECh. 1.3 - Prob. 20ECh. 1.3 - Prob. 21ECh. 1.3 - Prob. 22ECh. 1.4 - In Exercises 14, use EulersMethod to perform...Ch. 1.4 - In Exercises 14, use EulersMethod to perform...Ch. 1.4 - Prob. 3ECh. 1.4 - In Exercises 14, use EulersMethod to perform...Ch. 1.4 - In Exercises 510, use Euler’s method with the...Ch. 1.4 - In Exercises 510, use Euler’s method with the...Ch. 1.4 - Prob. 7ECh. 1.4 - Prob. 8ECh. 1.4 - Prob. 9ECh. 1.4 - Prob. 10ECh. 1.4 - Prob. 11ECh. 1.4 - Prob. 12ECh. 1.4 - Prob. 13ECh. 1.4 - Prob. 14ECh. 1.4 - Consider the initial-value problem dy/dt= y ,y(0)...Ch. 1.4 - Consider the initial-value problem dy/dt= 2 ...Ch. 1.4 - As we saw in Exercise 19 of Section 1.3, the...Ch. 1.4 - Prob. 18ECh. 1.4 - Prob. 19ECh. 1.4 - Prob. 20ECh. 1.4 - Prob. 21ECh. 1.5 - In Exercises 1—4, we refer to a function f, but we...Ch. 1.5 - Prob. 2ECh. 1.5 - In Exercises 1—4, we refer to a function f, but we...Ch. 1.5 - In Exercises 1—4, we refer to a function f, but we...Ch. 1.5 - Prob. 5ECh. 1.5 - In Exercises 5—8, an initial condition for the...Ch. 1.5 - Prob. 7ECh. 1.5 - In Exercises 5—8, an initial condition for the...Ch. 1.5 - (a) Show that y1(t)=t2 and y2(t)=t2+1 are...Ch. 1.5 - Consider the differential equation dy/dt=2y (a)...Ch. 1.5 - Consider the differential equation dydt=yt2 (a)...Ch. 1.5 - (a) Show that y1(t)=1t1 and y2(t)=1t2 are...Ch. 1.5 - Prob. 13ECh. 1.5 - In Exercises 13—16, an initial-value problem is...Ch. 1.5 - In Exercises 13—16, an initial-value problem is...Ch. 1.5 - In Exercises 13—16, an initial-value problem is...Ch. 1.5 - Prob. 17ECh. 1.5 - We have emphasized that the Uniqueness Theorem...Ch. 1.6 - In Exercises 112, sketch the phase lines for the...Ch. 1.6 - In Exercises 112, sketch the phase lines for the...Ch. 1.6 - Prob. 3ECh. 1.6 - In Exercises 112, sketch the phase lines for the...Ch. 1.6 - Prob. 5ECh. 1.6 - In Exercises 112, sketch the phase lines for the...Ch. 1.6 - In Exercises 112, sketch the phase lines for the...Ch. 1.6 - In Exercises 112, sketch the phase lines for the...Ch. 1.6 - Prob. 9ECh. 1.6 - In Exercises 112, sketch the phase lines for the...Ch. 1.6 - Prob. 11ECh. 1.6 - Prob. 12ECh. 1.6 - In Exercises 1321, a differential equation and...Ch. 1.6 - In Exercises 1321, a differential equation and...Ch. 1.6 - In Exercises 1321, a differential equation and...Ch. 1.6 - Prob. 16ECh. 1.6 - ]In Exercises 1321, a differential equation and...Ch. 1.6 - Prob. 18ECh. 1.6 - In Exercises 1321, a differential equation and...Ch. 1.6 - Prob. 20ECh. 1.6 - Prob. 21ECh. 1.6 - In Exercises 2227, describe the long-term behavior...Ch. 1.6 - Prob. 23ECh. 1.6 - In Exercises 2227, describe the long-term behavior...Ch. 1.6 - In Exercises 2227, describe the long-term behavior...Ch. 1.6 - In Exercises 2227, describe the long-term behavior...Ch. 1.6 - Prob. 27ECh. 1.6 - Prob. 28ECh. 1.6 - Prob. 29ECh. 1.6 - In Exercises 2932, the graph of a function f(y) is...Ch. 1.6 - In Exercises 2932, the graph of a function f(y) is...Ch. 1.6 - In Exercises 2932, the graph of a function f(y) is...Ch. 1.6 - Prob. 33ECh. 1.6 - Prob. 34ECh. 1.6 - Prob. 35ECh. 1.6 - Prob. 36ECh. 1.6 - Eight differential equations and four phase lines...Ch. 1.6 - Prob. 38ECh. 1.6 - Prob. 39ECh. 1.6 - Consider the Ermentrout-Kopell model for the...Ch. 1.6 - Prob. 41ECh. 1.6 - Prob. 42ECh. 1.6 - Prob. 43ECh. 1.6 - Prob. 44ECh. 1.6 - Let x(t) be the amount of time between two...Ch. 1.6 - Prob. 46ECh. 1.6 - Use the model in Exercise 45 to predict what...Ch. 1.6 - Prob. 48ECh. 1.7 - In Exercises 1-6, locate the bifurcation values...Ch. 1.7 - In Exercises 1-6, locate the bifurcation values...Ch. 1.7 - In Exercises 1-6, locate the bifurcation values...Ch. 1.7 - In Exercises 1-6, locate the bifurcation values...Ch. 1.7 - In Exercises 1-6, locate the bifurcation values...Ch. 1.7 - Prob. 6ECh. 1.7 - Prob. 7ECh. 1.7 - Prob. 8ECh. 1.7 - Prob. 9ECh. 1.7 - Prob. 10ECh. 1.7 - The graph to the right is the graph of a function...Ch. 1.7 - The graph to the right is the graph of a function...Ch. 1.7 - Six one-parameter families of different equations...Ch. 1.7 - Consider the Ermentrout-Kopell model for the...Ch. 1.7 - Prob. 15ECh. 1.7 - Sketch the graph of a function g(y) such that the...Ch. 1.7 - Is it possible to find a continuous function...Ch. 1.7 - Prob. 18ECh. 1.7 - Consider the population model dPdt=2PP250 for a...Ch. 1.7 - Prob. 20ECh. 1.7 - Prob. 21ECh. 1.7 - Prob. 22ECh. 1.7 - Prob. 23ECh. 1.8 - In Exercises 1-6, find the general solution of the...Ch. 1.8 - Prob. 2ECh. 1.8 - In Exercises 1-6, find the general solution of the...Ch. 1.8 - Prob. 4ECh. 1.8 - In Exercises 1-6, find the general solution of the...Ch. 1.8 - In Exercises 1-6, find the general solution of the...Ch. 1.8 - In Exercises 7-12, solve the given initial-value...Ch. 1.8 - In Exercises 7-12, solve the given initial-value...Ch. 1.8 - In Exercises 7-12, solve the given initial-value...Ch. 1.8 - In Exercises 7-12, solve the given initial-value...Ch. 1.8 - In Exercises 7-12, solve the given initial-value...Ch. 1.8 - In Exercises 7-12, solve the given initial-value...Ch. 1.8 - Consider the nonhomogeneous linear equation...Ch. 1.8 - Prob. 14ECh. 1.8 - Prob. 15ECh. 1.8 - Prob. 16ECh. 1.8 - Consider the nonlinear differential equation...Ch. 1.8 - Prob. 18ECh. 1.8 - Prob. 19ECh. 1.8 - Consider the nonhomogeneous linear equation...Ch. 1.8 - In Exercises 21-24, find the general solution and...Ch. 1.8 - In Exercises 21-24, find the general solution and...Ch. 1.8 - In Exercises 21-24, find the general solution and...Ch. 1.8 - In Exercises 21-24, find the general solution and...Ch. 1.8 - Prob. 25ECh. 1.8 - Prob. 26ECh. 1.8 - In Exercises 25-28, give a brief qualitative...Ch. 1.8 - Prob. 28ECh. 1.8 - A person initially places $1,000 in a savings...Ch. 1.8 - A student has saved $70,000 for her college...Ch. 1.8 - A college professor contributes $5,000 per year...Ch. 1.8 - Prob. 32ECh. 1.8 - Prob. 33ECh. 1.8 - Prob. 34ECh. 1.9 - In Exercises 1-6, find the general solution of the...Ch. 1.9 - In Exercises 1-6, find the general solution of the...Ch. 1.9 - In Exercises 1-6, find the general solution of the...Ch. 1.9 - In Exercises 1-6, find the general solution of the...Ch. 1.9 - In Exercises 1-6, find the general solution of the...Ch. 1.9 - In Exercises 1-6, find the general solution of the...Ch. 1.9 - In Exercises 7-12, solve the given initial-value...Ch. 1.9 - In Exercises 7-12, solve the given initial-value...Ch. 1.9 - Prob. 9ECh. 1.9 - Prob. 10ECh. 1.9 - Prob. 11ECh. 1.9 - In Exercises 7-12, solve the given initial-value...Ch. 1.9 - In Exercises 13-18, the differential equation is...Ch. 1.9 - Prob. 14ECh. 1.9 - Prob. 15ECh. 1.9 - Prob. 16ECh. 1.9 - Prob. 17ECh. 1.9 - Prob. 18ECh. 1.9 - Prob. 19ECh. 1.9 - Prob. 20ECh. 1.9 - Prob. 21ECh. 1.9 - Prob. 22ECh. 1.9 - Prob. 23ECh. 1.9 - A 30-gallon tank initially contains 15 gallons of...Ch. 1.9 - A 400-gallon tank initially contains 200 gallons...Ch. 1.9 - A 100-gallon tank initially contains loo gallons...Ch. 1.9 - Suppose a 50-gallon tank contains a volume Vo of...Ch. 1 - Short answer exercises: Exercises 1-10 focus on...Ch. 1 - Short answer exercises: Exercises 1-10 focus on...Ch. 1 - Short answer exercises: Exercises 1-10 focus on...Ch. 1 - Prob. 4RECh. 1 - Short answer exercises: Exercises 1-10 focus on...Ch. 1 - Short answer exercises: Exercises 1-10 focus on...Ch. 1 - Prob. 7RECh. 1 - Prob. 8RECh. 1 - Prob. 9RECh. 1 - Prob. 10RECh. 1 - Prob. 11RECh. 1 - Prob. 12RECh. 1 - Prob. 13RECh. 1 - Prob. 14RECh. 1 - True-false: For Exercises 11-20, determine if the...Ch. 1 - Prob. 16RECh. 1 - True-false: For Exercises 11-20, determine if the...Ch. 1 - Prob. 18RECh. 1 - Prob. 19RECh. 1 - Prob. 20RECh. 1 - Prob. 21RECh. 1 - Prob. 22RECh. 1 - Prob. 23RECh. 1 - Prob. 24RECh. 1 - Prob. 25RECh. 1 - Prob. 26RECh. 1 - Prob. 27RECh. 1 - Prob. 28RECh. 1 - In Exercises 21-29, (a) specify if the given...Ch. 1 - Prob. 30RECh. 1 - Prob. 31RECh. 1 - Prob. 32RECh. 1 - Prob. 33RECh. 1 - Prob. 34RECh. 1 - In Exercises 30-39, (a) specify if the given...Ch. 1 - Prob. 36RECh. 1 - Prob. 37RECh. 1 - Prob. 38RECh. 1 - Prob. 39RECh. 1 - Prob. 40RECh. 1 - Prob. 41RECh. 1 - Consider the autonomous differential equation...Ch. 1 - Prob. 43RECh. 1 - Prob. 44RECh. 1 - Prob. 45RECh. 1 - Prob. 46RECh. 1 - Prob. 47RECh. 1 - Prob. 48RECh. 1 - Eight differential equations and four slope fields...Ch. 1 - Prob. 50RECh. 1 - Prob. 51RECh. 1 - Consider the differential equation dy/dt=2ty2 ....Ch. 1 - Prob. 53RECh. 1 - A 1000-galIon tank initially contains a mixture of...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.Similar questions
- Temperature measurements are based on the transfer of heat between the sensor of a measuring device (such as an ordinary thermometer or the gasket of a thermocouple) and the medium whose temperature is to be measured. Once the sensor or thermometer is brought into contact with the medium, the sensor quickly receives (or loses, if warmer) heat and reaches thermal equilibrium with the medium. At that point the medium and the sensor are at the same temperature. The time required for thermal equilibrium to be established can vary from a fraction of a second to several minutes. Due to its small size and high conductivity it can be assumed that the sensor is at a uniform temperature at all times, and Newton's cooling law is applicable. Thermocouples are commonly used to measure the temperature of gas streams. The characteristics of the thermocouple junction and the gas stream are such that λ = hA/mc 0.02s-1. Initially, the thermocouple junction is at a temperature Ti and the gas stream at…arrow_forwardA body of mass m at the top of a 100 m high tower is thrown vertically upward with an initial velocity of 10 m/s. Assume that the air resistance FD acting on the body is proportional to the velocity V, so that FD=kV. Taking g = 9.75 m/s2 and k/m = 5 s, determine: a) what height the body will reach at the top of the tower, b) how long it will take the body to touch the ground, and c) the velocity of the body when it touches the ground.arrow_forwardA chemical reaction involving the interaction of two substances A and B to form a new compound X is called a second order reaction. In such cases it is observed that the rate of reaction (or the rate at which the new compound is formed) is proportional to the product of the remaining amounts of the two original substances. If a molecule of A and a molecule of B combine to form a molecule of X (i.e., the reaction equation is A + B ⮕ X), then the differential equation describing this specific reaction can be expressed as: dx/dt = k(a-x)(b-x) where k is a positive constant, a and b are the initial concentrations of the reactants A and B, respectively, and x(t) is the concentration of the new compound at any time t. Assuming that no amount of compound X is present at the start, obtain a relationship for x(t). What happens when t ⮕∞?arrow_forward
- Consider a body of mass m dropped from rest at t = 0. The body falls under the influence of gravity, and the air resistance FD opposing the motion is assumed to be proportional to the square of the velocity, so that FD = kV2. Call x the vertical distance and take the positive direction of the x-axis downward, with origin at the initial position of the body. Obtain relationships for the velocity and position of the body as a function of time t.arrow_forwardAssuming that the rate of change of the price P of a certain commodity is proportional to the difference between demand D and supply S at any time t, the differential equations describing the price fluctuations with respect to time can be expressed as: dP/dt = k(D - s) where k is the proportionality constant whose value depends on the specific commodity. Solve the above differential equation by expressing supply and demand as simply linear functions of price in the form S = aP - b and D = e - fParrow_forwardFind the area of the surface obtained by rotating the circle x² + y² = r² about the line y = r.arrow_forward
- 3) Recall that the power set of a set A is the set of all subsets of A: PA = {S: SC A}. Prove the following proposition. АСВ РАСРВarrow_forwardA sequence X = (xn) is said to be a contractive sequence if there is a constant 0 < C < 1 so that for all n = N. - |Xn+1 − xn| ≤ C|Xn — Xn−1| -arrow_forward3) Find the surface area of z -1≤ y ≤1 = 1 + x + y + x2 over the rectangle −2 ≤ x ≤ 1 and - Solution: TYPE YOUR SOLUTION HERE! ALSO: Generate a plot of the surface in Mathematica and include that plot in your solution!arrow_forward
- 7. Walkabout. Does this graph have an Euler circuit? If so, find one. If not, explain why not.arrow_forwardBelow, let A, B, and C be sets. 1) Prove (AUB) nC = (ANC) U (BNC).arrow_forwardQ1: find the Reliability of component in the system in fig(1) by minimal cut method. Q2: A component A with constant failure rate 1.5 per 1000 h, B per to 2 in 1000h, A and B in parallel, find the Reliability system? [ by exponential distribution]. Q3: Give an example to find the minimal path and estimate the reliability of this block diagram. Q4: By Tie set method find the Reliability of fig (2) FUZarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
01 - What Is A Differential Equation in Calculus? Learn to Solve Ordinary Differential Equations.; Author: Math and Science;https://www.youtube.com/watch?v=K80YEHQpx9g;License: Standard YouTube License, CC-BY
Higher Order Differential Equation with constant coefficient (GATE) (Part 1) l GATE 2018; Author: GATE Lectures by Dishank;https://www.youtube.com/watch?v=ODxP7BbqAjA;License: Standard YouTube License, CC-BY
Solution of Differential Equations and Initial Value Problems; Author: Jefril Amboy;https://www.youtube.com/watch?v=Q68sk7XS-dc;License: Standard YouTube License, CC-BY