What is the solution for y^{''}+5y^'-6y=2e^{-x} ?

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

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y^{''}+5y^'-6y=2e^{-x}

y^{^{''}} + 5 y^{^{'}} - 6 y = 2 e^{- x}

y = c_{1} e^{x} + c_{2} e^{- 6 x} - \frac{1}{5} e^{- x}

Solution steps

y^{''} (x) + 5 y^{'} (x) - 6 y = 2 e^{- x}

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- 6 x} - \frac{1}{5} e^{- x}

y = c_{1} e^{x} + c_{2} e^{- 6 x} - \frac{1}{5} e^{- x}

y^{^{''}} + 3 y^{^{'}} - y = t

y^{^{''}} - 5 y^{^{'}} + 4 y = 3 e^{x} sin (x)

y^{^{''}} - 4 y^{^{'}} + 4 y = e^{2 x} (12 x^{2} - 6 x)

y^{^{'''}} - 3 y^{^{''}} + 3 y^{^{'}} = x - 8 e^{x}

y^{^{'''}} - y^{^{''}} - 16 y^{^{'}} + 16 y = 9 - e^{x} + e^{4 x}

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