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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

\frac{\partial}{\partial x} (x^{3})

\int 2 + sin (x) d x

\int_{0}^{1} \frac{1}{x ^{1.2}} d x

- \frac{e ^{\frac{1}{x}}}{x ^{2}}

\int x \cdot ln (3 x) d x

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