For the following differential equation determine a suitable

For the following differential equation, determine a suitable form for the solution Y (t) if the method of undetermined coe cients is to be used. (Do not actually find the coe cients!) y\'\'-5y\'+6y=e^tsin2t+t^2cos3t

Solution

For e^t sin(2t) the guess is

e^t(A sin(2t)+B cos(2t))

For t^2 cos(3t) the guess is

(Et^2+Ft+G) cos(3t)+(Ht^2+J t+K)sin(3t)

So the form of the solution Y(t) is

e^t(A sin(2t)+B cos(2t))+(Et^2+Ft+G) cos(3t)+(Ht^2+J t+K)sin(3t)