What is the solution for (d^2y)/(dx^2)-(dy)/(dx)=x^2 ?

The solution for (d^2y)/(dx^2)-(dy)/(dx)=x^2 is y=c_{1}e^x+c_{2}-(x^3)/3-x^2-2x

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(d^2y)/(dx^2)-(dy)/(dx)=x^2

\frac{d ^{2} y}{d x ^{2}} - \frac{d y}{d x} = x^{2}

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} - \frac{d y}{d x} = x^{2}

Solve linear ODE:

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

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

y^{^{''}} + 4 y^{^{'}} + 4 y = \frac{e ^{- 2 x}}{x ^{2} + 1}

y^{^{''}} - 3 y^{^{'}} + 2 y = 5 e^{3 x}

y^{^{''}} - 16 y = e^{4 x}

y^{^{'''}} - 2 y^{^{''}} - y^{^{'}} + 2 y = e^{8 t}

\frac{d ^{2} y}{d x ^{2}} - k \frac{d y}{d x} = x e^{x}

What is the solution for (d^2y)/(dx^2)-(dy)/(dx)=x^2 ?
The solution for (d^2y)/(dx^2)-(dy)/(dx)=x^2 is y=c_{1}e^x+c_{2}-(x^3)/3-x^2-2x