What is the solution for y^{''}+3y^'+2y=6e^x ?

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

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y^{''}+3y^'+2y=6e^x

y^{^{''}} + 3 y^{^{'}} + 2 y = 6 e^{x}

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + e^{x}

Solution steps

y^{''} (x) + 3 y^{'} (x) + 2 y = 6 e^{x}

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + e^{x}

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + e^{x}

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