solve the given differential equations by writing the general solution. Write all of the steps of the solutions.

1. y" - 100 y = 3t² e^5t + cos t - t sint

2. 4y" + y = e-^2t sin( 0.5t) + 6t cos (0.5 t)

3. y" + 8y' + 16y = e^-4t + (t² + 5) e^-4t

4. Solve the given DE: y" + 4y' + 4y = te ^-2t