What is the solution for v^{''}-16v=2e^{4x} ?

The solution for v^{''}-16v=2e^{4x} is v(x)=c_{1}e^{4x}+c_{2}e^{-4x}+(e^{4x}x)/4

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v^{''}-16v=2e^{4x}

v^{^{''}} - 16 v = 2 e^{4 x}

v (x) = c_{1} e^{4 x} + c_{2} e^{- 4 x} + \frac{e ^{4 x} x}{4}

Solution steps

v^{''} (x) - 16 v (x) = 2 e^{4 x}

Solve linear ODE:

v (x) = c_{1} e^{4 x} + c_{2} e^{- 4 x} + \frac{e ^{4 x} x}{4}

v (x) = c_{1} e^{4 x} + c_{2} e^{- 4 x} + \frac{e ^{4 x} x}{4}

What is the solution for v^{''}-16v=2e^{4x} ?
The solution for v^{''}-16v=2e^{4x} is v(x)=c_{1}e^{4x}+c_{2}e^{-4x}+(e^{4x}x)/4