What is the solution for y^{''}-y^'-12y=(x+1)e^x ?

The solution for y^{''}-y^'-12y=(x+1)e^x is y=c_{1}e^{4x}+c_{2}e^{-3x}-(e^xx)/(12)-13/144 e^x

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y^{''}-y^'-12y=(x+1)e^x

y^{^{''}} - y^{^{'}} - 12 y = (x + 1) e^{x}

y = c_{1} e^{4 x} + c_{2} e^{- 3 x} - \frac{e ^{x} x}{12} - \frac{13}{144} e^{x}

Solution steps

y^{''} (x) - y^{'} (x) - 12 y = (x + 1) e^{x}

Solve linear ODE:

y = c_{1} e^{4 x} + c_{2} e^{- 3 x} - \frac{e ^{x} x}{12} - \frac{13}{144} e^{x}

y = c_{1} e^{4 x} + c_{2} e^{- 3 x} - \frac{e ^{x} x}{12} - \frac{13}{144} e^{x}

y^{^{''}} - 14 y^{^{'}} + 49 y = 35 x + 4

\frac{d ^{2} y}{d t ^{2}} + 4 y = sec^{2} (2 t)

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

y^{^{''}} + y = e^{t} + e^{- t}

3 \frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} + 2 = 0

What is the solution for y^{''}-y^'-12y=(x+1)e^x ?
The solution for y^{''}-y^'-12y=(x+1)e^x is y=c_{1}e^{4x}+c_{2}e^{-3x}-(e^xx)/(12)-13/144 e^x