Find the constants A and B in the solution y = Ae^x + Be^−xto the initial value problem: y′′ − y = 0,   y(0) = 2,   y′ (0) = 1

Q: Each of the following equations represents a cubic function

A: Given data: The first equation is y=2x2+3. The second equation is y=-x1/2-1. The third equation is…

Q: Let y₁ = xe-* be a solution of the equation y" + 2y' + y = 0. Find the second solution from y₁ by…

A: We know that if y1 be a solution to the second order homogeneous lineardifferential equation…

Q: show that y=x2 is one of this equation solutions x2y''-2y=0

A:

Q: Find the general solution to y''-1=0

A: y''-1 =0y'' = 1y' = ∫1 dxy' = x + By =∫(x + B) dxy = x22 + Bx + A

Q: Use undetermined coefficients to find the particular solution to y'' - 3y' + 2y = e(-26-24x)

A:

Q: Consider that Let the solution of equation y₁ = x² y2 = 3x² - y3 = 4x-2 2 x² x²y" + xy' 4y = 0…

A: All the parts are solved properly with detailed explanation.Hope you got your answer. If any query…

Q: Find all solutions of the equation x2y' = y3 − 5x2y3 explicitly

A:

Q: a) 2xy dx+(1+x²)dy=0 b) y'+(4/x)y=x* ------by exact method ---by linear method

A:

Q: Solve by shooting method.

A: The differential equation given is as follows: x2y'''-xy''+2y=2x3+2 The boundary conditions given…

Q: y y' + y? = x-2 X

A:

Q: Given the Bernoulli's equation Dy/DX+yP(x)=y^n Q(x) and x=y^1-n, reduce the equation to the linear…

A: Given differential equation is                                           dydx+yP(x)=ynQ(x);  x=y1-n…

Q: Suppose ay″+by′+cy=0 with y(0)=d and y′(0)=k has a general solution y=5e^(3x)−xe^(3x).   What are…

A:

Q: Find the general solution af the equation, y' = x(1- y).

A:

Q: How do I find the particular solution yp in the equation above?

A: For particular equation we will crate function for particular integral. Then we solve it by using…

Q: Solve 16y" – 8y" + y' = 0

A: Write the auxiliary equation first and find it's roots.

Q: Solve y' = 12xy 2х, у(0) — 15 -

A:

Q: Solve using method of undetermined coefficients: y" + y' - 2y = x². %3D

A: Solution :-

Q: Find the general solution to (t² + 4)y' + 2ty = t²(t² + 4). Enter your answer as y = .... Use C to…

A:

Q: Find the general solution of x2y" - (2a-1)xy' + a²y = xa+1 where a is a constant.

A: Given  x2y'' - 2a - 1xy + a2y = xa+1  ----------(1)           This is Cauchy's homogeneous…

Q: Ex. (9) Sol:- Solve 3y"-2y'+y= 4x+2

A:

Q: Solve: y' + 7y +9y' +9y=0 y(x)

A:

Q: Find the general solution of the equation

A:

Q: -1 -1 3. Find a particular solution of x' = -2 2 x+ 4 -1 -2 et

A:

Q: 7 0-3 -9 -2 3 18 0-8 y, y(0) = 2 3

A: Given y'=70-3-9-23180-8y Also given y0=23-1   To reduce to row echelon form and solve for constant…

Q: y" + 7y' + 10y = -1lte".

A:

Q: 5) Form a DE by eliminating the arbitrary constants from the equation y = asin(4x + 1).

A:

Q: Solve for the particular solution: x²y" - xy' - 3y = In x. Oyp = (In x)/3 - 2/9 yp = -x/3 + 2/9 Oyp…

A:

Q: y(4)+3y'''+2y''=12x2 High nonhomogeneous equations

A: