y^{''}-y=2(e^x-e^{-x})^{-1}

Lösung

y^{^{''}} - y = 2 (e^{x} - e^{- x})^{- 1}

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

Schritte zur Lösung

y^{''} (x) - y = 2 (e^{x} - e^{- x})^{- 1}

Solve linear ODE:

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

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

y^{^{''}} + 2 y = sec (x)

y^{^{''}} + 3 y^{^{'}} - 54 y = - 174 t + 108 t^{2}

2 y^{^{''}} + 5 y^{^{'}} + 3 y = \frac{1}{4} ln (x + 1)

y^{^{''}} + 9 y = 17 sec^{2} (3 t)

y^{^{''}} + 4 y^{^{'}} + 8 y = 8 x^{2} + 8 x + 1