What is the solution for y^{''}-y^'-6y=e^{3x} ?

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

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y^{''}-y^'-6y=e^{3x}

y^{^{''}} - y^{^{'}} - 6 y = e^{3 x}

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

Solution steps

y^{''} (x) - y^{'} (x) - 6 y = e^{3 x}

Solve linear ODE:

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

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

1 - e^{- 5 t}

4 x^{2} e^{x}

\int \frac{1}{x + x x} d x

\int_{1}^{x} \frac{1}{t} d t

x^{6 x}

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