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

The solution for 2y^{''}-3y^'+y=e^{-3x} is y=c_{1}e^x+c_{2}e^{x/2}+1/28 e^{-3x}

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

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

y = c_{1} e^{x} + c_{2} e^{\frac{x}{2}} + \frac{1}{28} e^{- 3 x}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{\frac{x}{2}} + \frac{1}{28} e^{- 3 x}

y = c_{1} e^{x} + c_{2} e^{\frac{x}{2}} + \frac{1}{28} e^{- 3 x}

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What is the solution for 2y^{''}-3y^'+y=e^{-3x} ?
The solution for 2y^{''}-3y^'+y=e^{-3x} is y=c_{1}e^x+c_{2}e^{x/2}+1/28 e^{-3x}