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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} - 2 y^{^{'}} + y = 4 e^{x}

y^{^{''}} + y^{^{'}} = n

y^{^{''}} + y^{^{'}} = 6

y^{^{''}} - 10 y^{^{'}} + 29 y = 87 x

(D + 1) 3 y = 5 e - x

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