Solve using the method of undetermined coefficient. Find the Yc and also the Yp. Y= Yp+Yc

For each of the following problems, find the general solution of the given differential equation. 1. y" - 2y' - 3y = (3t + 4)e2t 2. y" + 9y = te3t 3. y" - 2y' - 3y = -et 4. y" - 4y' + 3y = e3t 5. y" - 10y' + 25y = 6e-5t + t + 3 6. y" + 4y' + 4y = 2e2t - 6e-2t 7. y" +y' - 2y = 2t, y() = 0, y'(0) = 1 8. y" + 4y = 3et, y(0) = 0, y'(0) =2 9. y" - 5y' + 6y = e3t, y(0) = 3, y'(0) = 3 10. y" + 3y' = 2t2 + (t + 1)e-3t - Find a suitable form for yp(t), no need to calculate the coefficients. 11. y" + 6y' + 9y = (t2 + t)e-3t + t - Find a suitable form for yp (t), no need to calculate the coefficients. 12. y' + 3y' + 2y =4e ' + 5te-2t - Find a suitable form for Up(t), no need to calculate the coefficients. 13. y" + 6y' = t+ 4 + te2t -Find a suitable form for Up(t), no need to calculate the coefficients