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

Question

idealist10 · Answer

@SithsAndGiggles

freckles · Answer

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):
$$y''-7y'+12y=-e^{x}(17-42x) \ y''-7y'+12y=-e^{3x}$$

anonymous · Answer

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 $y_{p_2}=bxe^{3x}$.

idealist10 · Answer

Thank you!