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

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

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

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

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + \frac{1}{6} e^{x} + \frac{1}{12} e^{2 x}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + \frac{1}{6} e^{x} + \frac{1}{12} e^{2 x}

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + \frac{1}{6} e^{x} + \frac{1}{12} e^{2 x}

\int \frac{1}{3 x + 2} d x

\int_{0}^{2} (x - 3)^{2} - (x - 1)^{2} d x

(x + 1) y^{^{'}} + x y = 0

\frac{d}{d x} (\frac{2 x ^{2} - 1}{3 x ^{3} - 1})

\int e^{- x} sin^{2} (x) d x

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