What is the solution for y^{''}+5y^'-6y=xe^{(-5x)} ?

The solution for y^{''}+5y^'-6y=xe^{(-5x)} is y=c_{1}e^x+c_{2}e^{-6x}-(e^{-5x}x)/6+5/36 e^{-5x}

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

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

y = c_{1} e^{x} + c_{2} e^{- 6 x} - \frac{e ^{- 5 x} x}{6} + \frac{5}{36} e^{- 5 x}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- 6 x} - \frac{e ^{- 5 x} x}{6} + \frac{5}{36} e^{- 5 x}

y = c_{1} e^{x} + c_{2} e^{- 6 x} - \frac{e ^{- 5 x} x}{6} + \frac{5}{36} e^{- 5 x}

y^{^{''}} + 4 y = cos (t)

y^{^{'''}} + 5 y^{^{''}} + 6 y^{^{'}} = 4 + 9 sin (x)

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

y^{^{''''}} + 9 y^{^{''}} = cos (3 t)

y^{^{''}} - 2 y^{^{'}} + 5 y = 4 e^{3 t}

What is the solution for y^{''}+5y^'-6y=xe^{(-5x)} ?
The solution for y^{''}+5y^'-6y=xe^{(-5x)} is y=c_{1}e^x+c_{2}e^{-6x}-(e^{-5x}x)/6+5/36 e^{-5x}