What is the solution for y^{''}+y^'-12y=e^t+e^{2t}-1 ?

The solution for y^{''}+y^'-12y=e^t+e^{2t}-1 is y=c_{1}e^{3t}+c_{2}e^{-4t}-1/10 e^t-1/6 e^{2t}+1/12

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y^{''}+y^'-12y=e^t+e^{2t}-1

y^{^{''}} + y^{^{'}} - 12 y = e^{t} + e^{2 t} - 1

y = c_{1} e^{3 t} + c_{2} e^{- 4 t} - \frac{1}{10} e^{t} - \frac{1}{6} e^{2 t} + \frac{1}{12}

Solution steps

y^{''} (t) + y^{'} (t) - 12 y = e^{t} + e^{2 t} - 1

Solve linear ODE:

y = c_{1} e^{3 t} + c_{2} e^{- 4 t} - \frac{1}{10} e^{t} - \frac{1}{6} e^{2 t} + \frac{1}{12}

y = c_{1} e^{3 t} + c_{2} e^{- 4 t} - \frac{1}{10} e^{t} - \frac{1}{6} e^{2 t} + \frac{1}{12}

y^{^{'''}} + 100 y^{^{'}} = tan (10 x)

y^{^{''}} - 6 y^{^{'}} + 8 y = 5 x^{2} sin (4 x)

1 x^{^{''}} - 3 x^{^{'}} + 2 x = 20 sin (2 t)

y^{^{''}} + 4 y = 0.5

y^{^{'''}} + 2 y^{^{'}} = cos (x)

What is the solution for y^{''}+y^'-12y=e^t+e^{2t}-1 ?
The solution for y^{''}+y^'-12y=e^t+e^{2t}-1 is y=c_{1}e^{3t}+c_{2}e^{-4t}-1/10 e^t-1/6 e^{2t}+1/12