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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

5 y^{^{''}} + y^{^{'}} = 6 x

y^{^{''}} - 8 y^{^{'}} + 17 y = e^{4 x} - x^{2}

y^{^{''}} - 81 y = e^{10} t

y^{^{''}} - 7 y^{^{'}} + 6 y = sin (x)

3 \frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} - 4 y = 10 e^{- 3 x}

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