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

The solution for y^{''}+5y^'-6y=e^{2x} is y=c_{1}e^x+c_{2}e^{-6x}+1/8 e^{2x}

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

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

y = c_{1} e^{x} + c_{2} e^{- 6 x} + \frac{1}{8} e^{2 x}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- 6 x} + \frac{1}{8} e^{2 x}

y = c_{1} e^{x} + c_{2} e^{- 6 x} + \frac{1}{8} e^{2 x}

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} - 5 y = 5 x

2 y^{^{''}} + 50 y = 2 cos^{2} (5 x)

y^{^{''}} - y^{^{'}} - \frac{3}{4} y = cos (2 t)

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

y^{^{'''}} - 4 y^{^{'}} = x e^{2 x}

What is the solution for y^{''}+5y^'-6y=e^{2x} ?
The solution for y^{''}+5y^'-6y=e^{2x} is y=c_{1}e^x+c_{2}e^{-6x}+1/8 e^{2x}