(e^x)/(e^{2x)-4}dx=5ydy

Lösung

\frac{e ^{x}}{e ^{2 x} - 4} d x = 5 y d y

y = \frac{- ln ( \frac{e ^{x} + 2}{2} ) + ln ( \frac{e ^{x} - 2}{2} ) + c _{1}}{10}, y = - \frac{- ln ( \frac{e ^{x} + 2}{2} ) + ln ( \frac{e ^{x} - 2}{2} ) + c _{1}}{10}

Schritte zur Lösung

\frac{e ^{x}}{e ^{2 x} - 4} d x = 5 y d y

Solve separable ODE:

y = \frac{- ln ( \frac{e ^{x} + 2}{2} ) + ln ( \frac{e ^{x} - 2}{2} ) + c _{1}}{10}, y = - \frac{- ln ( \frac{e ^{x} + 2}{2} ) + ln ( \frac{e ^{x} - 2}{2} ) + c _{1}}{10}

y = \frac{- ln ( \frac{e ^{x} + 2}{2} ) + ln ( \frac{e ^{x} - 2}{2} ) + c _{1}}{10}, y = - \frac{- ln ( \frac{e ^{x} + 2}{2} ) + ln ( \frac{e ^{x} - 2}{2} ) + c _{1}}{10}

y = x y^{^{'}}

4 x y^{2} \frac{d y}{d x} = 3

\frac{d}{d x} (x y) = 0

\frac{d p}{d t} = p - p^{2}

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