What is the solution for y^{''}+6y^'+5y=3e^{-x} ?

The solution for y^{''}+6y^'+5y=3e^{-x} is y=c_{1}e^{-x}+c_{2}e^{-5x}+(3e^{-x}x)/4

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y^{''}+6y^'+5y=3e^{-x}

y^{^{''}} + 6 y^{^{'}} + 5 y = 3 e^{- x}

y = c_{1} e^{- x} + c_{2} e^{- 5 x} + \frac{3 e ^{- x} x}{4}

Solution steps

y^{''} (x) + 6 y^{'} (x) + 5 y = 3 e^{- x}

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} e^{- 5 x} + \frac{3 e ^{- x} x}{4}

y = c_{1} e^{- x} + c_{2} e^{- 5 x} + \frac{3 e ^{- x} x}{4}

y^{^{''}} + 4 y = tan (2 x) + 2

y^{^{''}} + y = 10 e^{2 x}

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

y^{^{''}} - 9 y^{^{'}} + 5 y = x e^{x}

4 y^{^{''}} - y^{^{'}} = 1

What is the solution for y^{''}+6y^'+5y=3e^{-x} ?
The solution for y^{''}+6y^'+5y=3e^{-x} is y=c_{1}e^{-x}+c_{2}e^{-5x}+(3e^{-x}x)/4