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

The solution for y^{''}-y^'-6y=2x is y=c_{1}e^{3x}+c_{2}e^{-2x}-x/3+1/18

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y^{''}-y^'-6y=2x

y^{^{''}} - y^{^{'}} - 6 y = 2 x

y = c_{1} e^{3 x} + c_{2} e^{- 2 x} - \frac{x}{3} + \frac{1}{18}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{- 2 x} - \frac{x}{3} + \frac{1}{18}

y = c_{1} e^{3 x} + c_{2} e^{- 2 x} - \frac{x}{3} + \frac{1}{18}

What is the solution for y^{''}-y^'-6y=2x ?
The solution for y^{''}-y^'-6y=2x is y=c_{1}e^{3x}+c_{2}e^{-2x}-x/3+1/18