What is the solution for (d^2y)/(dx^2)-4y^'-12y=2x+6 ?

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

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(d^2y)/(dx^2)-4y^'-12y=2x+6

\frac{d ^{2} y}{d x ^{2}} - 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^{^{'''}} - 3 y^{^{''}} + 4 y = 4 - e^{- 3 x}

x^{^{''}} + 5 x^{^{'}} + 4 x = 8 e^{t}

y^{^{''}} + 20 y^{^{'}} + 200 y = 1

y^{^{''}} + 20 y^{^{'}} + 200 y = 2

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

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