Diff. Eq. : Undetermined Coefficents

[NINHARDCOREFAN]

I have 2 problems that I'm not getting the right answer to:

y"+4y=3sin(2t)

I chose my guess to be: y=A[tsin(2t)]+B[tcos2t]
with this guess I'm getting only part of the answer right

I also tred this guess: y= A[t^2(sin(2t)]+ B[t^2(cos(2t)] + C[tsin(2t)]+D[tcos2t]

I got the same answer as above + some other weird answers


y"-y'-2y=(e^t+e^(-t))/2

I made this guess: Ae^t+Bte^(-t)

I got my answer as -2A=1/2 and -3B=1/2

However these were also wrong. Anything wrong with the guesses?

 

[Pyrrhus]

What were the fundamental (complimentary) set of solutions for each ODE?

 

[NINHARDCOREFAN]

Answers...

The first one: Asin(2t)+Bcos(2t)-(1/8)sin(2t)-(3/4)tcost(2t)
The second one : Ae^-t+Be^-2t+(1/6)te^(2t)+(1/8)e^(-2t)