Question

1. Find the general solution to the following ODE:

y′′′+ 4y′= sec(2x)

2. Find the solution to the following IVP:

2y′′+ 2y′−2y= 6x²−4x−1

y(0) = −32

y′(0) = 5

3. Verify that y₁=x^1/2ln(x) is a solution to

4x²y′′+y= 0,

and use reduction of order to find a second solution y₂.

4.

Find the general solutions to the following ODEs:

a) y′′′−y′= 0.

b) y′′+ 2y′+y= 0.

c) y′′−4y′+ 13y= 0.

Answer 1

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