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

The solution for y^{''}-y=x^2e^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^2e^x+5

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

\frac{5 s}{9 + s ^{2}}

\frac{5 x ^{3} + 3 x ^{2}}{x}

\frac{\partial}{\partial x} (x^{2} (1 - y^{\frac{2}{5}}))

y = x + x^{\frac{3}{2}} - 8 x

(5 x^{3} + 3 x y + 2 y^{2}) d x + (x^{2} + 2 x y) d y = 0

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