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}+c_{2}e^{-x}+(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} + c_{2} e^{- x} + \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} + c_{2} e^{- x} + \frac{x ^{3}}{3} - x^{2} + 2 x

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

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

y^{^{''}} + b y^{^{'}} + cy = e^{x} sin (x)

10 y^{^{''}} + 50 y^{^{'}} + 57.6 y = cos (x)

y^{^{''}} + y = 5 sin (4 x)

12 y^{^{''}} + 5 y^{^{'}} - 3 y = 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}+c_{2}e^{-x}+(x^3)/3-x^2+2x