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^{^{''}} + 7 y^{^{'}} + 12 y = t^{2} e^{- 3 t}

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

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

(d^{4} + d^{2}) y = 18 x - 4 sin (x)

y^{^{''}} + 6 y^{^{'}} + 5 y = 12 e^{t}, y (0) = - 1, y^{^{'}} (0) = 7

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}