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

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

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

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

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} + \frac{4}{5} e^{3 x}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} + \frac{4}{5} e^{3 x}

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} + \frac{4}{5} e^{3 x}

y^{^{''}} + 2 y^{^{'}} + y = g (t)

y^{^{''}} - 4 y^{^{'}} = 3 x e^{x} + 2

y^{^{''}} + 25 y = 8 cos (5 x) + 12 sin (5 x)

y^{^{''}} - 6 y^{^{'}} + 25 y = 2 sin (\frac{x}{2}) - cos (\frac{x}{2})

y^{^{''}} + 4 y^{^{'}} + 5 y = e^{- 2 x} sin (x)

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