What is the solution for y^{''}-y=x^2*e^x+5 ?

The solution for y^{''}-y=x^2*e^x+5 is y=c_{1}e^x+c_{2}e^{-x}+(e^xx^3)/6+(-e^xx^2+e^xx)/4-5

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y^{''}-y=x^2*e^x+5

y^{^{''}} - y = x^{2} \cdot e^{x} + 5

y = c_{1} e^{x} + c_{2} e^{- x} + \frac{e ^{x} x ^{3}}{6} + \frac{- e ^{x} x ^{2} + e ^{x} x}{4} - 5

Solution steps

y^{''} (x) - y = x^{2} \cdot e^{x} + 5

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} - 5

y = c_{1} e^{x} + c_{2} e^{- x} + \frac{e ^{x} x ^{3}}{6} + \frac{- e ^{x} x ^{2} + e ^{x} x}{4} - 5

y^{^{''}} + 5 y^{^{'}} + 6 y = 5 sin (x)

(d^{4} - 1) y = e^{x} cos (x)

y^{^{''}} - 2 y^{^{'}} = x^{2} - x

(d^{2} + 9) y = 7 e^{3 x} + 3 x^{2} + 4

y^{^{''}} - 2 y^{^{'}} + y = (3 x + 1) e^{x}

What is the solution for y^{''}-y=x^2*e^x+5 ?
The solution for y^{''}-y=x^2*e^x+5 is y=c_{1}e^x+c_{2}e^{-x}+(e^xx^3)/6+(-e^xx^2+e^xx)/4-5