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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

\int_{1}^{2} t ln (t) d t

\frac{d}{d x} ((5 x - 4) (2 x^{3} - x^{2} + 1))

f (x) = 9 e^{x} + x, (0, 9)

\int \frac{x ^{4}}{2} d x

\frac{d}{d x} (\frac{x sin ( x )}{1 + x})

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