Particular Solutions for Non-Homogeneous Differential Equations

[dspampi]

Find a particular solution for the following non-homogeneous dieren-
tial equation by the method of undetermined coefficients:

a. y'' + 8y' +12y = e^-2x + sin(2x)

b. y'' + 11y' - 12y = 3x^2 + 4 + e^x



I got for a. Yp(x) = 1/4xe^-2x + 1/40cos(2x) +1/20 sin(2x)

b. Yp(x) = -1/4x^2 - 11/24x - 229/288 - 1/13xe^-x

I have a feeling that a is right but not sure about b.

 

[LCKurtz]

Plug them back into the NH equation and see if they work. Then you will be sure.