Phasors and steady-state solutions

[ABoul]

Homework Statement

use phasors to evaluate the steady-state solution to the equation f'' + 1.5f' + f = Ce^2tj

Homework Equations

The Attempt at a Solution

let f = Ce^2tj (this is a 'trial solution', i think)

f' = 2tCe^2tj
f'' = 4(t^2)Ce^2tj

therefore 4(t^2)Ce^2tj + 3tCe^2jt + Ce^2tj = Ce^2tj
4t^2 + 3t = 0

therefore t = 0 and t = -3/4
therefore f = C and f = Ce^-1.5tj.

^ the above is NOTHING like the answer. what am i doing wrong?

 

[ABoul]

attempt #2:

f = Ae^2tj
f' = 2tAe^2tj
f'' = 4(t^2)Ae^2tj

so...

4(t^2)Ae^2tj + 3Ate^2tf + Ae^2tj = Ce^2tj

dividing through by e^2tj gives

A(4t^2 + 3t + 1) = C

so A = C/(4t^2 + 3t + 1)? that's still not the answer