What is the solution for y^{''}+2y^'+y=x^3 ?

The solution for y^{''}+2y^'+y=x^3 is y=c_{1}e^{-x}+c_{2}xe^{-x}+x^3-6x^2+18x-24

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y^{''}+2y^'+y=x^3

y^{^{''}} + 2 y^{^{'}} + y = x^{3}

y = c_{1} e^{- x} + c_{2} x e^{- x} + x^{3} - 6 x^{2} + 18 x - 24

Solution steps

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

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} x e^{- x} + x^{3} - 6 x^{2} + 18 x - 24

y = c_{1} e^{- x} + c_{2} x e^{- x} + x^{3} - 6 x^{2} + 18 x - 24

\int x 5 - x^{2} d x

\int e^{- s t} (3 t) d t

\int 5 x (x - x^{2}) d x

\frac{\partial}{\partial x} (ln (x^{2} + y) - z)

x \to 3 lim (x^{2} + 9)

What is the solution for y^{''}+2y^'+y=x^3 ?
The solution for y^{''}+2y^'+y=x^3 is y=c_{1}e^{-x}+c_{2}xe^{-x}+x^3-6x^2+18x-24