Question

Use the principle of superposition to find a particular solution of y"-7y'+12y=-e^(x)(17-42x)-e^(3x).

Answer 1

@SithsAndGiggles

Answer 2

Since it wants you to use principle of superposition I would break it like this:
solve both of the following (and then add the solutions together):
\[y''-7y'+12y=-e^{x}(17-42x) \\ y''-7y'+12y=-e^{3x}\]

Answer 3

Same procedure as before. Check the characteristic solution (\(r=3,r=4\)). One of these conflicts with the \(e^{3x}\) on the RHS.

Try using \(y_{p_1}=(a_0+a_1x)e^x\) and \(y_{p_2}=bxe^{3x}\).

Answer 4

Thank you!