(dy)/(dx)y=((x+1)/(x-1))^2

Lösung

\frac{d y}{d x} y = (\frac{x + 1}{x - 1})^{2}

y = 2 x + 8 (ln (x - 1) - \frac{1}{x - 1}) + c_{1}, y = - 2 x + 8 (ln (x - 1) - \frac{1}{x - 1}) + c_{1}

Schritte zur Lösung

\frac{d y}{d x} y = (\frac{x + 1}{x - 1})^{2}

Solve separable ODE:

y = 2 x + 8 (ln (x - 1) - \frac{1}{x - 1}) + c_{1}, y = - 2 x + 8 (ln (x - 1) - \frac{1}{x - 1}) + c_{1}

y = 2 x + 8 (ln (x - 1) - \frac{1}{x - 1}) + c_{1}, y = - 2 x + 8 (ln (x - 1) - \frac{1}{x - 1}) + c_{1}

x^{^{'}} = 2 + x + \frac{1}{4} x - \frac{1}{2}

e^{y} \cdot y^{^{'}} = \frac{3 x ^{2}}{1 + y}

\frac{d x}{d t} = - \frac{x}{100} + 125

\frac{d y}{d t} = y^{2} e^{- t}, y (0) = \frac{1}{2}, t \geq 0

f (x) = \frac{1}{1 + x ^{2}} f^{^{'}} (x)