15. If y is the solution to the initial value problem 1 y' – y = x, 2x I> 0, and y(1) = 3' then y(4) is

Q: 5. Find a second solution to (1 – a2) y" + 2xy' = 0, given one solution y1(x) = 1.

A:

Q: (9) Find the general solution of 1 y" + =y' = 12 In(x) x2

A: The detailed solution with step by step explanation is written belowExplanation:Step 1: Step 2: Step…

Q: c. y' + 2y = x³ with y(1) = 2 Yo (x) = e Yp (x) = y (x) = y (x) = -2x 1½ e ²x³ - 2/ ( 10²x² -…

A:

Q: Find a continous solution satisfying the equation and the initial condition (1+x²)y/ +2.ry = P(x) r,…

A: we have given a first order differential equation with piecewise function P(x) we need to find a…

Q: Solve the IVP y''+ 5y'+6y=2cost subject to y (0) = 1 and y'(0) = 0.

A: The given initial value problem is y''+5y'+6y=2cost subject to y0=1 and y'0=0. Solve this initial…

Q: Find an explicit solution 2x y'=. y(0) = -2 y+x²y'

A: The given differential equation is       y' = 2x/(y + x2y)      => dy/dx = 2x/{y(1 + x2)}…

Q: Find the solution to  x' = y - x + t y' = y if x(0) = 2 and y(0) = 4 x(t) = ? y(t) = ?

A:

Q: 4. Use undetermined coefficients to find a particular solution to x=2x+3y+5, y' = 2x + y = 2t.

A: Approach to solving the question:To find a particular solution to the system of differential…

Q: Solve the initial value problem given by y' = (x2 + 2y2)/(xy) ,  y(1) = 1 What is the interval of…

A:

Q: Find the solution to x' = y y' = 12x + 1y if x(0) = 0 and y(0) = 8

A:

Q: Find the solution to the following initial value problem y" + 5y′ − 6y = 0, y(0) = 0, y′(0) = 7.

A: Given differential equation is Then the corresponding auxiliary equation isTherefore, the general…

Q: What is the solution of y2 - x2y'=0 with IVP y(1)=1/2 ?

A:

Q: What is the solution to the IVP? y''+y'+4y=0      y(0)=1     y'(0)=-1

A:

Q: 10. Particular solution of y"-4y' + 8y = x³, when x = 0, y = 2, y' = 4

A: We have to find the particular solution of y''-4y'+8y=x3,  when x=0, y=2, y'=4.

Q: Find the solution of y' + p(x) = 4x if y(0) = 3 and where

A:

Q: Solve Cauchi problem x²y" - xy + y = 0. y(1) = 0, y'(1) = 1

A:

Q: 3. Find the solution of the initial value problem xy" + y' = x²(y/)², y(1) = 0, y'(1) = 1. What is…

A:

Q: Solve the inital value problem 2xy'+y=6x  for x is greater than 0 y(4)=26

A: Given:           2xy'+y=6x ;   x>0,  y(4)=26

Q: Solve the equation y"+y=S(t-2π), y(0) = 0, y'(0) = 1

A:

Q: The solution to y' = 4y - 8 with y(0) = 5 is A. y = 5e¹x C. y = 3e¹x + 2 B. y = 8ex-3 D. y = 4e* +1

A:

Q: 6 3x -7x +3 Find y' if y=

A:

Q: Show that y = - In x + 3x - 5 is a solution of y" -=0. Use y = - Inx+3x – 5 to find y' and y". y' =O

A:

Q: What is the particular solution of y'=x²-2x+3, ify=4whenx=0?

A: What is Ordinary DIfferential Equation: A differential equation having one or more functions of one…

Q: Would you mind giving a brief explaning alongside each of these components (a-h) and how they fit on…

A:

Q: For each scenario, identify the appropriate growth model that describes how it's changing. v The…

A: #> To solve these questions we need to have a few ideas about the Linear and Exponential growth…

Q: 4. Solve for Y (s) given ty" + y' + ty = 0 y(0) = 0 %3D

A:

Q: 4. Solve Cauchy problem: y" - 5y' + 4y = 0, y(0) = 1, y'(0) = 2

A: To solve the following Cauchy problem.

Q: Verify (do not solve) that y(x) = 3x + 2x-1/3 is a solution to 3xy' + y = 12x.

A: Solution is    y(x) = 3x + 2x-1/3 Now to verify differentiate the solution w.r.to x .

Q: 8. Use Green's functions to find a solution to the IVP x²y" - 2xy + 2y = 2x² In x, y(1) = 1, y'(1) =…

A:

Q: Find the general solution of the following DE. y' = 3 (y + 1) O y = 3ce³x - 1 Oy = ce³x - 1 Oy =…

A: y' = 3(y+1) dy/dx = 3(y+1) dy/3(y+1) = dx dy/(y+1) = 3dx now apply both side integration

Q: If the solution to the initial value problem y' + ay = 0, y(0) = b passes through the points (2, 2)…

A: Given data

Q: 3. Determine the general solution to the equation xy' = (1+ x) sec(y), x > 0. You can leave your…

A:

Q: 3. What is the particular solution if y(1) = 0 • xy' = y+ (x² + y²) ||

A: Given:- xy' = y+(x2+y2)1/2 y(1) = 0  To find:- Particular solution of given differential equation

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.