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

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

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y^{''}-5y^'-6y=xe-5x

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

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

Solution steps

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

Solve linear ODE:

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

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

\frac{5}{2} x^{^{''}} + 10 x^{^{'}} + 20 x = 200, x (0) = 0

\frac{1}{8} y^{^{''}} + 8 x + 4 y^{^{'}} = 0, y^{^{'}} (0) = 9, y (0) = 0

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} + 1 = 0

y^{^{''}} - 16 y = cos (4 t), y (0) = 0, y^{^{'}} (0) = 2

2 y^{^{''}} - y^{^{'}} - 3 y = 3 x e^{2 x}, y (0) = 1, y^{^{'}} (0) = 0

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