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

The solution for y^{''}+y^'-6y=2e^{5x} is y=c_{1}e^{2x}+c_{2}e^{-3x}+1/12 e^{5x}

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

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

y = c_{1} e^{2 x} + c_{2} e^{- 3 x} + \frac{1}{12} e^{5 x}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- 3 x} + \frac{1}{12} e^{5 x}

y = c_{1} e^{2 x} + c_{2} e^{- 3 x} + \frac{1}{12} e^{5 x}

\frac{\partial}{\partial x} (y e^{(x^{2} - y)})

y = 29 x

2 y^{^{''}} + 3 y^{^{'}} - 2 y = 0

\frac{\partial}{\partial x} (e^{x y} + x y e^{x y})

\frac{d y}{d x} = \frac{4 x ^{4} y + 6 y ^{5}}{2 x ^{5} + 3 x y ^{4}}

What is the solution for y^{''}+y^'-6y=2e^{5x} ?
The solution for y^{''}+y^'-6y=2e^{5x} is y=c_{1}e^{2x}+c_{2}e^{-3x}+1/12 e^{5x}