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

The solution for y^{''}-y=x^2ex+5 is y=c_{1}e^x+c_{2}e^{-x}-ex^3-6ex-5

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y^{''}-y=x^2ex+5

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} - 2 y^{^{'}} + 2 y = 1

y^{^{''}} - 4 y^{^{'}} + 5 y = 2 e^{x}

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

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

\frac{1}{2} q^{^{''}} + 10 q^{^{'}} + (\frac{1}{1 0 ^{- 2}}) q = 200

What is the solution for y^{''}-y=x^2ex+5 ?
The solution for y^{''}-y=x^2ex+5 is y=c_{1}e^x+c_{2}e^{-x}-ex^3-6ex-5