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

The solution for y^{'''}-6y^{''}-y^'+6y=e^{5x} is y=c_{1}e^{6x}+c_{2}e^{-x}+c_{3}e^x-1/24 e^{5x}

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

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

y = c_{1} e^{6 x} + c_{2} e^{- x} + c_{3} e^{x} - \frac{1}{24} e^{5 x}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{6 x} + c_{2} e^{- x} + c_{3} e^{x} - \frac{1}{24} e^{5 x}

y = c_{1} e^{6 x} + c_{2} e^{- x} + c_{3} e^{x} - \frac{1}{24} e^{5 x}

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

y^{^{''}} - 4 \cdot y = e^{- α \cdot x}

y^{^{'''}} + 3 y^{^{''}} + 2 y^{^{'}} = (x^{2} + 4 x + 8) e^{2} x

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

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

What is the solution for y^{'''}-6y^{''}-y^'+6y=e^{5x} ?
The solution for y^{'''}-6y^{''}-y^'+6y=e^{5x} is y=c_{1}e^{6x}+c_{2}e^{-x}+c_{3}e^x-1/24 e^{5x}