What is the solution for y^{''}-9y=e^{(-2x)}(-17+10x) ?

The solution for y^{''}-9y=e^{(-2x)}(-17+10x) is y=c_{1}e^{3x}+c_{2}e^{-3x}-2xe^{-2x}+5e^{-2x}

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y^{''}-9y=e^{(-2x)}(-17+10x)

y^{^{''}} - 9 y = e^{(- 2 x)} (- 17 + 10 x)

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

Solution steps

y^{''} (x) - 9 y = e^{(- 2 x)} (- 17 + 10 x)

Solve linear ODE:

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

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

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

y^{^{''}} + 5 y = - 9.81

y^{^{''}} + 4 y^{^{'}} + 4 y = 3 e^{- 3 x}

\frac{d ^{2} y}{d x ^{2}} + 5 \frac{d y}{d x} + 6 y = x e^{3 x}

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

What is the solution for y^{''}-9y=e^{(-2x)}(-17+10x) ?
The solution for y^{''}-9y=e^{(-2x)}(-17+10x) is y=c_{1}e^{3x}+c_{2}e^{-3x}-2xe^{-2x}+5e^{-2x}