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

The solution for y^{''}+3y^'=-e^{2x}+e^{3x} is y=c_{1}+c_{2}e^{-3x}-1/10 e^{2x}+1/18 e^{3x}

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

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

y = c_{1} + c_{2} e^{- 3 x} - \frac{1}{10} e^{2 x} + \frac{1}{18} e^{3 x}

Solution steps

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

Solve linear ODE:

y = c_{1} + c_{2} e^{- 3 x} - \frac{1}{10} e^{2 x} + \frac{1}{18} e^{3 x}

y = c_{1} + c_{2} e^{- 3 x} - \frac{1}{10} e^{2 x} + \frac{1}{18} e^{3 x}

What is the solution for y^{''}+3y^'=-e^{2x}+e^{3x} ?
The solution for y^{''}+3y^'=-e^{2x}+e^{3x} is y=c_{1}+c_{2}e^{-3x}-1/10 e^{2x}+1/18 e^{3x}