3-  (a) solve the given differential equation  y''' - y'' -4y' +4y = 1-e^x  (b) without solving. What is the form of a particular solution of  y'''-y''-4y'+4y =0

Q: show that function  y1=x-1 is a special solution of the differential equation y'=1 - ( y-x+1)2 and…

A: Given the differential equation y’ = 1 – ( y – x + 1)2 and we have to show that y  = x -1 is a…

Q: 2. A chemical reaction proceeds in such a way that after the first second, the amount of a certain…

A: Given state of change of a chemical is indirectly proportional to the product of mass and time.To…

Q: (4) Form the differential equation by eliminating the arbitrary constants a and b from y=ae +be¯ª.

A:

Q: 20.Find the particular solution of the differential equation x (+1) - x-2y, given x -1 when y = 3

A:

Q: 1. Find real-valued fundamental solutions of the differential equation 1 x' = Ax, A= 2 %3D 4 -3

A: We need to find the solutions of given differential equations. Given - X' = AX, where A = 1-24-3 So,…

Q: III. dy y³ dx x²y-xyz

A: Sol:- y' =y3x2y-xy2Substitute y=vx, v is a function of xxv' +v=v21-vRewrite in the form of a first…

Q: (4) a general solution of the 4th-order differential equation y +y(3) + y" = 0.

A:

Q: 2-The exact solution of differential equation ý--4y with y(0)-1 is (a) 2e-4x (b) e-4x (c) e-4x +1…

A: As per as our guideline i am supposed to answer only one question from all these question . To get…

Q: Show that the function  y1=x-1 is a special solution of the differential equation y'=1-(y-x+1)2 and…

A:

Q: xy"+y'=0; y1=ln(x) How can this second-order differential equation be solved by general solution?

A:

Q: Solve the 1st order differential equation y3+x-1 y = x dx

A: Given differential equation is y3dydx+x-1y4=x. Note that the differential equation is of the form…

Q: 4: A- Solve the differential equation subjected to the condition y0)=1 dx

A: Firstly separate the variables and integrate on both sides and solve the differential equation.…

Q: II. dy dx 2x² x(y² + 1)

A: We have to find the best way to solve the given First Order Differential Equation by Finding…

Q: Consider the initial-value problem (x² − 1)y"+y' + y = ex y(1) = 1 y' (1) = -1 Does the Existence…

A:

Q: Solve for the General Solution of the given Differential Equation y' = y – xy³e- -2x

A:

Q: What is the solution of the first order differential equation y(k + 1) = y(k) + 5.

A:

Q: у" - у' - бу %3D 0

A:

Q: у" - 2у' + у %3D et + Зех 1+x2

A:

Q: 5. If the characteristic equation of the differential equation 27 - 184 dx +8- y-0 is dx 27m -18m…

A: The characteristic equation of the given differential equation is 27m4-18m2+8m-1=0.

Q: The rate of growth of a plant is proportional to the difference between its height h and the maximum…

A: The given data is: The rate of growth of a plant is proportional to the difference between its…

Q: A population in a certain city in 1990 is 1.4 million people, and satisfiesthe differential…

A: A differential equation represents the relation between a variable, and it's derivative. Solution of…

Q: 5. A differential equation is if it can be written in the form f(y)d(y) = g(x)d(x)-

A: A differential equation is ORDINARY if it can be  Written in the form f(y)dy = g(x) dx .

Q: (9x^2 + y - 1) - (4y - x)y′ = 0

A:

Q: Q-2. Form the first-order differential equation of ey = sinx

A:

Q: Suppose that a large mixing tank initially holds 900 gallons of water in which 50 pounds of salt…

A:

Q: Find the general or Special Solution to the differential equation 2 y = (x-y₁²

A:

Q: 2.Form the differential equation from the family of curves y² = Ae³* + Be* , where A and B are…

A:

Q: Yp = -1 / 5ex - 1/2 (cos 2x) ((ln (sec2x + tan2x)) is the particular solution of the differential…

A: A solution yp(x) of a differential equation that contains no arbitrary constants is called a…

Q: Solve the non-homogeneous differential equation of 6y"-y'-y=1-x-x?

A: Given differential equation is  6y"-y'-y=1-x-x2

Q: Solve the first order differential equation. (3x - y - 4)dy - (x + y - 4)dx = 0

A:

Q: Suppose that a large mixing tank initially holds 300 gallons of water in which 50 pounds of salt…

A: To Determine -

Q: 5. (a) Find the particular solution of the differential equation x³ = 1-e²t if x(0) = 2.

A:

Q: 2. Solve the differential equation- + x, with y(1) = 1.

A:

Q: 2. A chemical reaction proceeds in such a way that after the first second, the amount of a certain…

A:

Q: find the solution of differential equation 2 y3 y' +- y

A:

Q: The solution of the following homogenous differential equation y' = - x+y -is

A: We find the solution of the homogeneous differential equation y'=yx+y

Q: Choose a solution for the differential equation y'' - y = x2ex + 5: e-x(1/6x3 - 1/4 x2 + 1/4x + 3)…

A: Given non- homogeneous differential equation,y''-y=x2ex+5  ...(1). Solving the homogeneous part:…

Q: The differential equation: y²x + y² = x²yy' is solved by

A:

Q: The number of arbitrary constants in the particular solution of a differential equation of third…

A:

Q: y" – 2y' + y = -3 - x+x².

A:

Q: 8- The solution of differential equation y" + 4y = 0 is.

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Suppose that a large mixing tank initially holds 300 gallons of water in which 50 pounds of salt…

A:

Q: Suppose that a large mixing tank initially holds 700 gallons of water in which 50 pounds of salt…

A: Given: A tank containing 700 gallons of water in which 50 pounds of salt is dissolved. Rate at which…

Q: Solve the Homogenous Differential Equation: (x² + y³) = xy ху.

A: This question is based on solution of Homogeneous differential equation.

Q: 1. Solve given separable differential equation: y' + 2x(y² - 3y + 2) = 0

A: Let us consider the differential equation of the form  dydx=f(x)g(y) Solving the equation using the…

Q: 3. a. Solve the differential equation y'= 2x√/1-y² b. Explain why the initial value problem y'=…

A:

Q: 2. Suppose a large mixing tank initially holds 300 gallons of water in which 40 lbs of salt have…

A:

Q: 1. Discuss or show the methods in solving Exact and Non-Exact Differential Equations.

A:

Q: 2. | Determine the general solution of the given differential equation y" -6y" = 3- cos x

A: The solution is given as

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.