Find a particular solution of?

Question

Find a particular solution of y"-2y'+y=-e^(x)[(3+4x-x^2)cosx+(3-4x-x^2)sinx].

 

I need to do this problem by the method of undetermined coefficients. What's the correct initial guess for this problem and how can you find the correct initial guess? The answer is yp=e^(x)(1-x^2)(cosx+sinx).

Answer 1

Haven't you asked about this before?

 

Try using the guess:

 

y_p = e^x cos x (A + Bx + Cx²) + e^x sin x (D + Ex + Fx²).

 

I believe I explained already why this initial guess is necessary. Let me know if you need more help with the reasoning. The basic idea is to include enough terms so that you can get everything you need to calculate the right side of the DE.