What is the solution for y^{''}+7y^'+12y=5e^{-6x} ?

The solution for y^{''}+7y^'+12y=5e^{-6x} is y=c_{1}e^{-3x}+c_{2}e^{-4x}+5/6 e^{-6x}

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y^{''}+7y^'+12y=5e^{-6x}

y^{^{''}} + 7 y^{^{'}} + 12 y = 5 e^{- 6 x}

y = c_{1} e^{- 3 x} + c_{2} e^{- 4 x} + \frac{5}{6} e^{- 6 x}

Solution steps

y^{''} (x) + 7 y^{'} (x) + 12 y = 5 e^{- 6 x}

Solve linear ODE:

y = c_{1} e^{- 3 x} + c_{2} e^{- 4 x} + \frac{5}{6} e^{- 6 x}

y = c_{1} e^{- 3 x} + c_{2} e^{- 4 x} + \frac{5}{6} e^{- 6 x}

What is the solution for y^{''}+7y^'+12y=5e^{-6x} ?
The solution for y^{''}+7y^'+12y=5e^{-6x} is y=c_{1}e^{-3x}+c_{2}e^{-4x}+5/6 e^{-6x}