What is the solution for y^{''}-y^'-6y=50e^{-2x} ?

The solution for y^{''}-y^'-6y=50e^{-2x} is y=c_{1}e^{3x}+c_{2}e^{-2x}-10xe^{-2x}

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y^{''}-y^'-6y=50e^{-2x}

y^{^{''}} - y^{^{'}} - 6 y = 50 e^{- 2 x}

y = c_{1} e^{3 x} + c_{2} e^{- 2 x} - 10 x e^{- 2 x}

Solution steps

y^{''} (x) - y^{'} (x) - 6 y = 50 e^{- 2 x}

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{- 2 x} - 10 x e^{- 2 x}

y = c_{1} e^{3 x} + c_{2} e^{- 2 x} - 10 x e^{- 2 x}

y^{^{''}} + 4 y^{^{'}} + 5 y = e^{- 4 x}, y (0) = - 2, y^{^{'}} (0) = 1

y^{^{''}} - 24 y^{^{'}} + 9 = 0, y (1) = 0, y^{^{'}} (1) = 1

y^{^{''}} + 2 y^{^{'}} - 3 y = 6 e^{- 2 x}

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

y^{^{''}} + 16 y = sec^{3} (4 t)

What is the solution for y^{''}-y^'-6y=50e^{-2x} ?
The solution for y^{''}-y^'-6y=50e^{-2x} is y=c_{1}e^{3x}+c_{2}e^{-2x}-10xe^{-2x}