Question

Find a particular solution of y"-2y'+2y=e^(x)[(2-2x-6x^2)cosx+(2-10x+6x^2)sinx].

Answer 1

r^2-2r+2=0
r=1+/-I
So \[y=C _{1}e ^{x}sinx+C _{2}e ^{x}cosx\]

Answer 2

So what's the correct initial guess?

Answer 3

@hartnn

Answer 4

maybe
\(Y= e^x (Ax^3+Bx^2+Cx+D) \cos x +e^x (Ex^3+Fx^2+Gx+H) \sin x\)
because differentiating x^3 terms will give x^2 terms..

Answer 5

You reminded me of something, from your initial guess, I formed my correct initial guess based on your initial guess. So thank you for the help, I got the right answer!