What is the solution for y^{''}-2y^'-12y=2x+6 ?

The solution for y^{''}-2y^'-12y=2x+6 is y=c_{1}e^{(1+sqrt(13))x}+c_{2}e^{(1-sqrt(13))x}-x/6-17/36

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y^{''}-2y^'-12y=2x+6

y^{^{''}} - 2 y^{^{'}} - 12 y = 2 x + 6

y = c_{1} e^{(1 + 13) x} + c_{2} e^{(1 - 13) x} - \frac{x}{6} - \frac{17}{36}

Solution steps

y^{''} (x) - 2 y^{'} (x) - 12 y = 2 x + 6

Solve linear ODE:

y = c_{1} e^{(1 + 13) x} + c_{2} e^{(1 - 13) x} - \frac{x}{6} - \frac{17}{36}

y = c_{1} e^{(1 + 13) x} + c_{2} e^{(1 - 13) x} - \frac{x}{6} - \frac{17}{36}

y^{^{''}} - 3 y^{^{'}} + 2 y = 2 e^{- 5 t}

y^{^{''}} - 2 y - 3 y = 4 e^{x} - 9

y^{^{''}} + 25 y = cos (4 x)

y^{^{''}} - y^{^{'}} - 6 y = 69 cos (3 x)

\frac{d ^{3} y}{d x ^{3}} + \frac{d y}{d x} = e^{x}

What is the solution for y^{''}-2y^'-12y=2x+6 ?
The solution for y^{''}-2y^'-12y=2x+6 is y=c_{1}e^{(1+sqrt(13))x}+c_{2}e^{(1-sqrt(13))x}-x/6-17/36