Use Euler's method to obtain a four-decimal approxcimation of the indicated value. First use h = 0.1 and then use h = 0.05. Find an explicit solution for the initial-value problem and then fill in the following tables. (Round your answers to four decimal places. Percentages may be rounded to two decimal places. Use the rounded values for subsequent calculations.) y- y, y(0) - 1; y(1.0) vlx) = (explicit solution) h = 0.1 Actual Value Absolute % Rel. Error Ya Error 0.00 1.0000 1.0000 0.0000 0.00 1.1025 0.0027 0.10 1.1052 024 0.20 1.2155 1.2214 0.48 0.30 1.2401 1.3499 0.0008 0.73 0.40 1.4775 1.4918 0.0120 0.85 0.50 1.6290 1.6487 0.0197 1.10 0.60 1.7000 1.8221 0.0201 1.43 0.70 1.9801 2.0138 0.0337 1.67 0.80 2.1831 2.2255 0.0424 1.91 0.90 2.4000 2.4596 0.0527 2.14 1.00 2.7183

Use Euler's method to obtain a four-decimal approxcimation of the indicated value. First use h = 0.1 and then use h = 0.05. Find an explicit solution for the initial-value problem and then fill in the following tables. (Round your answers to four decimal places. Percentages may be rounded to two decimal places. Use the rounded values for subsequent calculations.) y- y, y(0) - 1; y(1.0) vlx) = (explicit solution) h = 0.1 Actual Value Absolute % Rel. Error Ya Error 0.00 1.0000 1.0000 0.0000 0.00 1.1025 0.0027 0.10 1.1052 024 0.20 1.2155 1.2214 0.48 0.30 1.2401 1.3499 0.0008 0.73 0.40 1.4775 1.4918 0.0120 0.85 0.50 1.6290 1.6487 0.0197 1.10 0.60 1.7000 1.8221 0.0201 1.43 0.70 1.9801 2.0138 0.0337 1.67 0.80 2.1831 2.2255 0.0424 1.91 0.90 2.4000 2.4596 0.0527 2.14 1.00 2.7183

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.7: Applications

Problem 13EQ

See similar textbooks

Related questions

Q: Solve the following initial value problem and leave the solution in implicit form. Use graphing…

A: Consider the function

Q: Consider the initial value problem, y" + y' – 6y = 0, y(0) = 10, y'(0) = 0 %3D %3D Determine the…

A: Given differential equation is linear homogeneous differential equation with constant coefficients…

Q: Solve the following initial value problem and present its particular solution: ?"+?′+9.25?=0,…

Q: Consider the initial value problem, x²y" – 3xy' + 4y = 0, y(1) = –n, y'(1) = 27 Determine the value…

Q: Solve the following initial value problem: t? + 4 y(1) = 1. 3t3 + 4t2 –4t Please select file(s)…

A: The given function is y'=t2+43t2+4t2-4tWe can write it asdydt=t2+43t2+4t2-4tdy=t2+43t2+4t2-4tdt…

Q: Use Euler's method to obtain a four-decimal approximation of the indicated value. First use h = 0.1…

A: Solve the differential equation. y'=2xydydx=2xydyy=2xdx∫dyy=∫2xdxln y=2∫xdxln y=2x22+Cln y=x2+C

Q: Find the function ?(?)f(x) described by the given initial value problem. ?″(?)=0, ?′(−2)=4,…

Q: Solve the following initial value problem. y' – 5y +6y=e; y(0)=0, y(0) =2 Find the value of y(t) if…

A: To solve the given initial value problem.

Q: Find the general solution and when initial conditions are given, get the corresponding particular…

A: Given differential equation is, cotxsin8ydx-sin2(4y)sin2x-25dy=0.

Q: Using Euler's Method, approximate the initial value problem for various values of x given in the…

Q: Solve the following initial value problem and present its particular solution: y"+y′+0.25y=0,…

A: First find the auxiliary equation then find the roots of auxiliary equation here the roots are…

Q: Solve the initial-value problem for x as a function of t. dx (2t3 – 2t? + t – 1) 12, г (2) — 0

A: Given,

Q: Solve the following initial value problem: y? DE: ty' = ty+ nd Initial value: y(e) = 12e. %3D Then…

Q: a.Find the first five nonzero terms in the solution of the given initial-value problem. b. Plot the…

Q: In the following problem use Euler’s method to calculate the first three approximations to the…

A: Given Data The derivative equation is y'=y21+2x. Th differential value of x is dx=0.5. y(-1)=1.…

Q: 1. Employ the Heun's method to solve x .y=1, using a step size of 0.7 and y(1)=5 dx and determine…

Q: Using Euler's Method, approximate the initial value problem for various values of x given in the…

A: Let us approximate the initial value problem for various values of x given in the table using…

Q: Given dp/dt=cp(1-p)-ep. Given that p represents the fraction of islands occupied, 0 < p < 1. Let c…

A: Solution: Consider the given equation is dpdt = cp1-p-ep where p represents the fraction of islands…

Q: Solve the following initial value problem: 2y" + 3y" – 3y' – 2y = e", y(0) = 0, y'(0) = 0, y"(0) = 1…

Q: solve the given initial value problem. Sketch the graph of the solution and describe its behavior…

Q: 14. Starting with the initial value x = and using Newton-Raphson procedure once, an approximation to…

A: According to our company policy, we are supposed to answer only one ( first) question. For the rest…

Q: If $6000 is invested at 5% compounded continuously, what is the amount after 2 years? Which of the…

Q: x" + 4x'+ 3x = 72t + 100 e3", x(0) = 1, x'(0) = 2 Solve the above IVP and then find x(0.25). Put…

A: The given differential equation is x''+4x'+3x=72t+100e-3t, x0=1,x'0=2. The auxiliary equation is…

Q: Using Euler's Method, approximate the initial value problem for various values of x given in the…

A: Given differential equation is dydx=9x2-4x+5, y(-1)=0 step size h = 0.2 initial values:…

Q: (a) Check that the function y(z) = r + 2r+2 is a solution to this initial value problem. (b) Use…

A: Hello. Since your question has multiple parts, we will solve the first part for you. If you want…

Q: Solve the following initial value problem. y" – 3y' + 2y = e4, y(0) = 1, =..2 - | Find the value of…

Q: Textbook e Videos [+] Solve the following initial-value problems starting from yo = 9. dy -7y dt A.…

Q: Solve the following initial value problem and leave the solution in implicit form. Use graphing…

A: To solve y'x=1+x2-y; y1=1

Q: Find approximate values of the solution of the initial value problem given below att = 0.5, 1.0,…

A: Given that y'=0.5-t+2y, y(0)=1 Where F=0.5-t+2y . (i) If h=0.025, From euler formula,…

Q: Q-the Newton raphson method is applied to find the root of f(x)= x* -1 with an initial guess Xo =0.5…

A: Given function is, fx=x2-1......(1)fxn=xn2-1....2 Differentiating the equation (1) up to first order…

Q: A student would like to calculate an approximate value for v15 using the Newton- Raphson method with…

A: The absolute approximate error is given as | x3 - x2 | = |3.8731 - 3.8966 | = 0.0235 To find value…

Q: Solve the given initial-value problem. dx-x - x = 5y², x(9) = 1 x(x) = 51,² – 404 y Give the largest…

A: To solve the given differential equation.

Q: The equation of motion of a mass is given as: y= (0.51)e 0.-(0.01)e.2, where y is the displacement…

Q: Solve the given initial-value problem. di + Ri= E₁ i(0) = lor L, R, E, io constants dt i(t) = Give…

Q: Q-the Newton raphson method is applied to find the root of f(x)= x² -1 with an initial guess xo =0.5…

Q: Use the Euler method to solve the following equation analytically for five iterations. Given that…

Q: Use Euler's method to approximate y(1.9). Start with step size h=0.1, and then use successively…

A: Euler's Method: Let the initial value problem is given as y'=f(x,y) , y(x0)=y0. Then the…

Q: Solve the following initial value problem. dr de = -лсоs л0, г(1)=2 (Type an exact answer, using as…

A: We have to find the initial value problem.

Q: Determine whether the following equation are separable. If so, solve the initial value problem.…

A: We have to determine whether the equation is separable: y't=ety, y0=1. Rewriting the given…

Q: Suppose the initial population is Po = 220, the point of inflection is (16,1600), and the time is…

A: We are given that the initial population is P0=220, the point of inflection is (16, 1600), and the…

Q: What is the initial population? By what percentage does the population grow each year?

Q: In the following problem use Euler’s method to calculate the first three approximations to the…

A: Given: y'=1-yxy2=-1 and dx=0.5 To Find: (a). Use Euler’s method to calculate the first three…

Q: Solve the given initial-value problem. xy' + y = e*, y(1) = 8 y(x) = Give the largest interval I…

Q: Solve the initiall- value problem: - Cad- Smスtみ o<メsos, Using Adams- Moulton method w0rking to s…

A: Given - dydx = cosx - sinx + y , 0 ≤ x ≤ 0.5 , y0 = 0 To find - Solve the initial - value problem…

Q: Solve the given initial-value problem. xy' + y = e*, y(1) = 6 y(x) = Give the largest interval I…

Q: Solve the following initial value problem and present its particular solution: y" + y' + 0.25y = 0,…

A: The given initial value problem is: y''+y'+0.25y=0 ; y(0)=3, y'(0)=-3.5

Q: Consider the initial value problem, y" + y' – 6y = 0, y(0) = 10, y'(0) = 0 Determine the value of…

Q: Solve the following initial value problem for y = f (x). dy dx = e−3x, y = 79 when x =…

A: dydx=e-3x and y=79 whrn x=0

Q: Solve the following initial value problem: æ" +w?x = Fsin(wt) (0) = 0, a'(0) = 0

Q: Let A= (11). It can be shown that etA - et Use this fact to write the solution to the initial value…

A: Given that A=1101 and y(0)=01.

Concept explainers

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

Question

I dont know what the explicit solution is or how to figure it out

Use Euler's method to obtain a four-decimal approximation of the indicated value. First use h = 0.1 and then use h = 0.05. Find an explicit solution for the initial-value problem and then fill in the following tables. (Round your answers to four decimal places. Percentages may be rounded to two decimal
places. Use the rounded values for subsequent calculations.)
y' = y, y(0) = 1; y(1.0)
y(x) =
(explicit solution)
h = 0.1
Actual
Value
Absolute
% Rel.
Error
Error
0.00
1.0000
1.0000
0.0000
0.00
0.10
1.1025
1.1052
0.0027
0.24
0.20
1.2155
1.2214
0/0050
0.48
0.30
1.2401
1.3499
0.0008
0.73
0.40
1.4775
1.4918
0.0120
0.85
0.50
1.6290
1.6487
0.0197
1.19
0.60
1.7980
1.8221
0.0261
1,43
0.70
1.9801
2.0138
0.0337
1.67
0.80
2.1831
2.2255
0.0424
1.91
0.90
2.4069
2.4596
0.0527
2.14
1.00
2.7183

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Step 7

Trending now

This is a popular solution!

Step by step

Solved in 7 steps with 7 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Linear Equations$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

Repeat the previous exercise to find the formula forthe APY of an account that compounds daily. Usethe results from this and the previous exercise todevelop a function I(n)for the APY of any accountthat compounds n times per year.
Use the differential to approximate each quantity. Then use a calculator to approximate the quantity, and give the absolute value of the difference the two results to 4decimal places. e0.002
A plug gage tapers 3.10 mm along a 38.00 mm length, as shown in Figure 215. Set up a proportion and determine the amount of taper in the workpiece for each of the following problems. Express the answers to 2 decimal places.
Use the total differential to approximate each quantity. Then use a calculator to approximate the quantity, and give the absolute value of the differences in the two results to 4decimal places. 1.03e0.04.
Estimate the age of a newly discovered fossil for which the ratio of carbon-14 to carbon-12 is R=1/1014.