What is the solution for y^{''}-y^'-12y=5e^{2x}-4 ?

The solution for y^{''}-y^'-12y=5e^{2x}-4 is y=c_{1}e^{4x}+c_{2}e^{-3x}-1/2 e^{2x}+1/3

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y^{''}-y^'-12y=5e^{2x}-4

y^{^{''}} - y^{^{'}} - 12 y = 5 e^{2 x} - 4

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

Solution steps

y^{''} (x) - y^{'} (x) - 12 y = 5 e^{2 x} - 4

Solve linear ODE:

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

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

What is the solution for y^{''}-y^'-12y=5e^{2x}-4 ?
The solution for y^{''}-y^'-12y=5e^{2x}-4 is y=c_{1}e^{4x}+c_{2}e^{-3x}-1/2 e^{2x}+1/3