Find a particular solution of y"+3y'-2y=e^(-2x)[(4+20x)cos3x+(26-32x)sin3x].

Question

idealist10 · Answer

$$y _{p}=e ^{-2x}(A+Bx)(\cos3x+\sin3x)$$

idealist10 · Answer

Is my initial guess right above?

idealist10 · Answer

@myininaya @Luigi0210

myininaya · Answer

what the scooby 
that right hand side is monstrous

myininaya · Answer

i think that looks like a fine guess

idealist10 · Answer

Because the answer is $$y _{p}=e ^{-2x}(1-2x)(\cos3x-\sin3x)$$

idealist10 · Answer

If the guess looks fine, then I'll try it.

myininaya · Answer

you could throw in some more constant values
$$y_p=e^{-2x}(Ax+B)( C \cos(3x)+D \sin(3x))$$

idealist10 · Answer

Okay, cool. While this may take time, I'll do the problem and tell you what I got.

myininaya · Answer

if you try the first one and it fails
see if that one works 
my guess is that last one work due to your - sign between the cos(3x) and the sin(3x)

idealist10 · Answer

I tried the second one which you suggested and it worked perfectly! Thank you so much for the help! God, that problem took a very long time to solve. But I'm happy. :)