What is the solution for y^{''}-4y^'-12y=2x+6 ?

The solution for y^{''}-4y^'-12y=2x+6 is y=c_{1}e^{6x}+c_{2}e^{-2x}-x/6-4/9

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y^{''}-4y^'-12y=2x+6

y^{^{''}} - 4 y^{^{'}} - 12 y = 2 x + 6

y = c_{1} e^{6 x} + c_{2} e^{- 2 x} - \frac{x}{6} - \frac{4}{9}

Solution steps

y^{''} (x) - 4 y^{'} (x) - 12 y = 2 x + 6

Solve linear ODE:

y = c_{1} e^{6 x} + c_{2} e^{- 2 x} - \frac{x}{6} - \frac{4}{9}

y = c_{1} e^{6 x} + c_{2} e^{- 2 x} - \frac{x}{6} - \frac{4}{9}

y^{^{''}} + 4 y^{^{'}} + 4 y = x^{2} e^{- 2 x} + 1

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

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

y^{^{''}} - 2 y^{^{'}} - 3 y = 4 e^{x} - 6

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

What is the solution for y^{''}-4y^'-12y=2x+6 ?
The solution for y^{''}-4y^'-12y=2x+6 is y=c_{1}e^{6x}+c_{2}e^{-2x}-x/6-4/9