What is the solution for y^{''}-4y^'-12y=t-6 ?

The solution for y^{''}-4y^'-12y=t-6 is y=c_{1}e^{6t}+c_{2}e^{-2t}-t/(12)+19/36

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y^{''}-4y^'-12y=t-6

y^{^{''}} - 4 y^{^{'}} - 12 y = t - 6

y = c_{1} e^{6 t} + c_{2} e^{- 2 t} - \frac{t}{12} + \frac{19}{36}

Solution steps

y^{''} (t) - 4 y^{'} (t) - 12 y = t - 6

Solve linear ODE:

y = c_{1} e^{6 t} + c_{2} e^{- 2 t} - \frac{t}{12} + \frac{19}{36}

y = c_{1} e^{6 t} + c_{2} e^{- 2 t} - \frac{t}{12} + \frac{19}{36}

What is the solution for y^{''}-4y^'-12y=t-6 ?
The solution for y^{''}-4y^'-12y=t-6 is y=c_{1}e^{6t}+c_{2}e^{-2t}-t/(12)+19/36