What is the solution for x^{''}-x^'-6x=8 ?

The solution for x^{''}-x^'-6x=8 is x=c_{1}e^{3t}+c_{2}e^{-2t}-4/3

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x^{''}-x^'-6x=8

x^{^{''}} - x^{^{'}} - 6 x = 8

x = c_{1} e^{3 t} + c_{2} e^{- 2 t} - \frac{4}{3}

Solution steps

x^{''} (t) - x^{'} (t) - 6 x = 8

Solve linear ODE:

x = c_{1} e^{3 t} + c_{2} e^{- 2 t} - \frac{4}{3}

x = c_{1} e^{3 t} + c_{2} e^{- 2 t} - \frac{4}{3}

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

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

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

y^{^{''}} - y^{^{'}} - 2 y = 3 x + 6

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

What is the solution for x^{''}-x^'-6x=8 ?
The solution for x^{''}-x^'-6x=8 is x=c_{1}e^{3t}+c_{2}e^{-2t}-4/3