Question

Find a particular solution of y"+3y'+y=(2-6x)cosx-9sinx.

Answer 1

@zepdrix @Preetha @pooja195 @TheSmartOne

Answer 2

@thomaster @Luigi0210 @johnweldon1993

Answer 3

Hmm I forget...
Our right side contains both polynomial stuff AND cosine sine.
So I think our particular solution will be of the form:
product of a first degree polynomial and cosines and sines,\[\rm y_p=(A+Bx)(C \cos x+D \sin x)\quad=\quad AC \cos x+AD \sin x+BC x \cos x+BD x \sin x\]Relabeling the constants for convenience,\[\large\rm y_p=A \cos x+B \sin x+ Cx \cos x+ D x \sin x\]

Answer 4

And then differentiating that is going to be a paaaaain lol

Answer 5

I dunno if this helps or not, but this is my work for part of the problem.
It gives us a system of 4 equations and 4 unknowns which is going to be solvable.

Probably easier to approach the problem using the other method...
I forget what it's called, using that weird Wronskian thing 0_o

But this way isn't too bad.

Answer 6

Thank you for the help!