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

The solution for y^{''}-y=sinh(x) is y=c_{1}e^x+c_{2}e^{-x}+(2e^xx+2e^{-x}x-8sinh(x)-e^{-x}+e^x)/8

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y^{''}-y=sinh(x)

y^{^{''}} - y = sinh (x)

y = c_{1} e^{x} + c_{2} e^{- x} + \frac{2 e ^{x} x + 2 e ^{- x} x - 8 sinh ( x ) - e ^{- x} + e ^{x}}{8}

Solution steps

y^{''} (x) - y = sinh (x)

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- x} + \frac{2 e ^{x} x + 2 e ^{- x} x - 8 sinh ( x ) - e ^{- x} + e ^{x}}{8}

y = c_{1} e^{x} + c_{2} e^{- x} + \frac{2 e ^{x} x + 2 e ^{- x} x - 8 sinh ( x ) - e ^{- x} + e ^{x}}{8}

What is the solution for y^{''}-y=sinh(x) ?
The solution for y^{''}-y=sinh(x) is y=c_{1}e^x+c_{2}e^{-x}+(2e^xx+2e^{-x}x-8sinh(x)-e^{-x}+e^x)/8