What is the solution for y^{''}-y=(e^{2x}-e^{-2x})/2 ?

The solution for y^{''}-y=(e^{2x}-e^{-2x})/2 is y=c_{1}e^x+c_{2}e^{-x}+(e^{2x}-e^{-2x})/6

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

y^{^{''}} - y = \frac{e ^{2 x} - e ^{- 2 x}}{2}

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

Solution steps

y^{''} (x) - y = \frac{e ^{2 x} - e ^{- 2 x}}{2}

Solve linear ODE:

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

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

What is the solution for y^{''}-y=(e^{2x}-e^{-2x})/2 ?
The solution for y^{''}-y=(e^{2x}-e^{-2x})/2 is y=c_{1}e^x+c_{2}e^{-x}+(e^{2x}-e^{-2x})/6