What is the solution for y^{''}-4y=e^{3x} ?

The solution for y^{''}-4y=e^{3x} is y=c_{1}e^{2x}+c_{2}e^{-2x}+1/5 e^{3x}

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y^{''}-4y=e^{3x}

y^{^{''}} - 4 y = e^{3 x}

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} + \frac{1}{5} e^{3 x}

Solution steps

y^{''} (x) - 4 y = e^{3 x}

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} + \frac{1}{5} e^{3 x}

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} + \frac{1}{5} e^{3 x}

What is the solution for y^{''}-4y=e^{3x} ?
The solution for y^{''}-4y=e^{3x} is y=c_{1}e^{2x}+c_{2}e^{-2x}+1/5 e^{3x}