What is the solution for y^{''}-y=8xe^x ?

The solution for y^{''}-y=8xe^x is y=c_{1}e^x+c_{2}e^{-x}+2x^2e^x-2e^xx

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y^{''}-y=8xe^x

y^{^{''}} - y = 8 x e^{x}

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

Solution steps

y^{''} (x) - y = 8 x e^{x}

Solve linear ODE:

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

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

x \to 1 lim (7^{x^{4} - x^{2}})

\int_{0}^{1} ln (x + 1) d x

y = \frac{( 4 x ^{2} + 6 x + 8 )}{x}

- 4 e^{- \frac{x}{3}} - 2

f (x) = - \frac{9}{2} x^{2} + 7 x + 7, at x = - 1

What is the solution for y^{''}-y=8xe^x ?
The solution for y^{''}-y=8xe^x is y=c_{1}e^x+c_{2}e^{-x}+2x^2e^x-2e^xx