What is the solution for y^{''}-4y=2e^{4t} ?

The solution for y^{''}-4y=2e^{4t} is y=c_{1}e^{2t}+c_{2}e^{-2t}+1/6 e^{4t}

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y^{''}-4y=2e^{4t}

y^{^{''}} - 4 y = 2 e^{4 t}

y = c_{1} e^{2 t} + c_{2} e^{- 2 t} + \frac{1}{6} e^{4 t}

Solution steps

y^{''} (t) - 4 y = 2 e^{4 t}

Solve linear ODE:

y = c_{1} e^{2 t} + c_{2} e^{- 2 t} + \frac{1}{6} e^{4 t}

y = c_{1} e^{2 t} + c_{2} e^{- 2 t} + \frac{1}{6} e^{4 t}

What is the solution for y^{''}-4y=2e^{4t} ?
The solution for y^{''}-4y=2e^{4t} is y=c_{1}e^{2t}+c_{2}e^{-2t}+1/6 e^{4t}