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

y^{^{''}} - 2 y^{^{'}} - 3 y = 24 t e^{2 t}

y^{^{''}} - y^{^{'}} - 6 y = - 468 sin (3 t)

3 y^{^{''}} - 4 y^{^{'}} + y = 5

y^{^{''}} - 4 y^{^{'}} + 4 y = e^{- x} (9 x^{2} - 3 x - 4)

(D^{2} + 2 D + 1) y = \frac{e ^{- x}}{x}

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