8. Solve the IVP y" – 2y' + 2y = 0, y(0) = 2 and y'(0) = 0.

Q: B. Solve x' = 01 1 54 x + 12e4t 18e4t

A:

Q: Solve 2y'' - 5y' - 25y = 0, y(0) = 0, y’(0) = = y(t) = - 37.5

A:

Q: Solve y" +5y' = (2x+1)e" -5x

A:

Q: 1. Solve Cauchy-Euler equation. r²y" – ry' + y = 2x

A:

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

A:

Q: 3. Solve using any technique y" – 2y/ – 3y = 3e",; 7 ", y(0) = 3, y'(0)

A: We have to solve given problem:

Q: 3. Solve y" – 2y' + 5y = 0, y(0) = 5, y'(0) = –3. %3D

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: -4x y"+6y'+9y=7+

A:

Q: Solve the IVP y′′ + 2y′ + 5y = 8e^(−t), y(0) = 0, y′(0) = 8

A:

Q: 6. Solve the IVP with y(1) = 2 and ty' = 4t² - 2y.

A:

Q: Solve y" -8y' +16y = 0

A:

Q: y' = (4x + y)?

A:

Q: Find an explicit solution for y′ = ye^−x^2 , y(0) = 1

A: The given differential equation is y'=ye-x2 and the initial condition is y(0)=1. Simplify the given…

Q: 5. Solve 2y" - 3y' - 2y = 0; y(0) = 1, y'(0) = -1.

A:

Q: Solve the following IVP. y"'-5y"-22+56=0 y(0)=1 y'(0)=-2 y''(0

A:

Q: 2. Solve y" + 2y' – 3y = 3, y(0) = y'(0) = 1. II %3D %3D

A: given differential equation is linear non homogeneous differential equation with constant…