Question

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).

Answer 1

lmLtfy:

\[ y''+y=e^{-x}(2-4x+2x^2)+e^{3x}(8-12x-10x^2)\]

Answer 2

principle of superposition :

Answer 3

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.

Answer 4

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.

Answer 5

Thank you for the help, it worked!