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

Lösung

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

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} + 8 y = 8 e^{- 2 x}

y^{^{'''}} - y^{^{''}} = 2 cos (x)

y^{^{''}} - y^{^{'}} - 12 y = 98 (x + 2) e^{- 3 x}

y^{^{''}} + 2 y^{^{'}} + y = (\frac{1}{6}) e^{- x}

y^{^{'''}} + 2 y^{^{''}} - y^{^{'}} - 2 y = 5 H (t)