y^{''}-y=(1-e^{2x})^{-3/2}

Lösung

y^{^{''}} - y = (1 - e^{2 x})^{- \frac{3}{2}}

y = c_{1} e^{x} + c_{2} e^{- x} + e^{x} \cdot \int \frac{e ^{- x}}{2 ( 1 - e ^{2 x} ) ^{\frac{3}{2}}} d x - \frac{1}{2 ( 1 - e ^{2 x} ) ^{\frac{1}{2}}}

Schritte zur Lösung

y^{''} (x) - y = (1 - e^{2 x})^{- \frac{3}{2}}

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- x} + e^{x} \cdot \int \frac{e ^{- x}}{2 ( 1 - e ^{2 x} ) ^{\frac{3}{2}}} d x - \frac{1}{2 ( 1 - e ^{2 x} ) ^{\frac{1}{2}}}

y = c_{1} e^{x} + c_{2} e^{- x} + e^{x} \cdot \int \frac{e ^{- x}}{2 ( 1 - e ^{2 x} ) ^{\frac{3}{2}}} d x - \frac{1}{2 ( 1 - e ^{2 x} ) ^{\frac{1}{2}}}

y^{^{''}} + 4 y^{^{'}} - 2 y = x^{3}

(d^{2} + d - 6) y = e^{- 3} x

y^{^{'''}} - 5 y^{^{''}} = 2 x

y^{^{''}} - 2 y^{^{'}} - 3 y = e t, y (0) = 2, y^{^{'}} (0) = 4

x^{^{''}} + 23.04 x = 2 cos (5 t)