What is the solution for y^{''}-y^'-6y=20e^{-2x} ?

The solution for y^{''}-y^'-6y=20e^{-2x} is y=c_{1}e^{3x}+c_{2}e^{-2x}-4xe^{-2x}

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y^{''}-y^'-6y=20e^{-2x}

y^{^{''}} - y^{^{'}} - 6 y = 20 e^{- 2 x}

y = c_{1} e^{3 x} + c_{2} e^{- 2 x} - 4 x e^{- 2 x}

Solution steps

y^{''} (x) - y^{'} (x) - 6 y = 20 e^{- 2 x}

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{- 2 x} - 4 x e^{- 2 x}

y = c_{1} e^{3 x} + c_{2} e^{- 2 x} - 4 x e^{- 2 x}

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2 y^{^{'''}} + 3 y^{^{''}} - 8 y^{^{'}} + 3 y = 0

\frac{x ^{2}}{4}

\int_{4}^{6} 2 π (y) (\frac{4}{y}) d y

\frac{d}{d x} (x^{2} + 1 - x)

What is the solution for y^{''}-y^'-6y=20e^{-2x} ?
The solution for y^{''}-y^'-6y=20e^{-2x} is y=c_{1}e^{3x}+c_{2}e^{-2x}-4xe^{-2x}