Use the principle of superposition to find a particular solution of y"+y=e^(-x)(2-4x+2x^2)+e^(3x)(8-12x-10x^2).

Question

irishboy123 · Answer

lmLtfy:

$$ y''+y=e^{-x}(2-4x+2x^2)+e^{3x}(8-12x-10x^2)$$

ganeshie8 · Answer

principle of superposition :
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thomas5267 · Answer

For $y''+y=e^{-x}(2-4x+2x^2)$, make a guess of the form $y_{p1}=e^{-x}(c_1+c_2x+c_3x^2)$.  The answer for this part is very nice.

thomas5267 · Answer

For $y''+y=e^{3x}(8-12x-10x^2)$, make a guess of the form $y_{p2}=e^{3x}(d_1+d_2x+d_3x^2)$.  Not as nice as the first part but still pretty nice.

idealist10 · Answer

Thank you for the help, it worked!