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

The solution for y^{''}-y^'-12y=e^{2x}+e^x-2 is y=c_{1}e^{4x}+c_{2}e^{-3x}-1/10 e^{2x}-1/12 e^x+1/6

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y^{''}-y^'-12y=e^{2x}+e^x-2

y^{^{''}} - y^{^{'}} - 12 y = e^{2 x} + e^{x} - 2

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

Solution steps

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

Solve linear ODE:

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

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

What is the solution for y^{''}-y^'-12y=e^{2x}+e^x-2 ?
The solution for y^{''}-y^'-12y=e^{2x}+e^x-2 is y=c_{1}e^{4x}+c_{2}e^{-3x}-1/10 e^{2x}-1/12 e^x+1/6