What is the solution for y^{''}-y=x^2e^x+9 ?

The solution for y^{''}-y=x^2e^x+9 is y=c_{1}e^x+c_{2}e^{-x}+(e^xx^3)/6+(-e^xx^2+e^xx)/4-9

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y^{''}-y=x^2e^x+9

y^{^{''}} - y = x^{2} e^{x} + 9

y = c_{1} e^{x} + c_{2} e^{- x} + \frac{e ^{x} x ^{3}}{6} + \frac{- e ^{x} x ^{2} + e ^{x} x}{4} - 9

Solution steps

y^{''} (x) - y = x^{2} e^{x} + 9

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- x} + \frac{e ^{x} x ^{3}}{6} + \frac{- e ^{x} x ^{2} + e ^{x} x}{4} - 9

y = c_{1} e^{x} + c_{2} e^{- x} + \frac{e ^{x} x ^{3}}{6} + \frac{- e ^{x} x ^{2} + e ^{x} x}{4} - 9

What is the solution for y^{''}-y=x^2e^x+9 ?
The solution for y^{''}-y=x^2e^x+9 is y=c_{1}e^x+c_{2}e^{-x}+(e^xx^3)/6+(-e^xx^2+e^xx)/4-9