Second order non-homogeneous linear diff equations:

Variation of Parameters:   Formula derivation

1. Find the general solution of the diff equations.

a. \(y''-3y'+2y=3e^t\) solution

b. \(y''-2y'=3e^{2t}\) solution

c. \( y''+4y=3\csc{t} \)  solution

d. \( y''+9y=2\sec^2{3t} \)  solution

2. Find the solution of the ODE by variation of parameters (do not use formula).

a. \(\displaystyle y''-2y'+y=t^{-1}e^t \)   solution

b. \(\displaystyle y''-5y'+6y=2e^t \)   solution

c. \(\displaystyle y''+16y=\sec(4t) \)   solution