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=x1/2ln(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.
Find the general solution y = C1Y1 +
C2 Y2 + Yp to the
ODE
y'' + y' − 2y = − 2x + 4 y (0) = − 4, y' (0) = − 7
Y = ?
Please show your work step by step. Thank you!