y(1-x^2)dy-x(1-y^2)dx=0

Lösung

y (1 - x^{2}) d y - x (1 - y^{2}) d x = 0

y = e^{- 2 c_{1}} - e^{- 2 c_{1}} x^{2} + 1, y = - e^{- 2 c_{1}} - e^{- 2 c_{1}} x^{2} + 1

Schritte zur Lösung

y (1 - x^{2}) d y - x (1 - y^{2}) d x = 0

Solve separable ODE:

y = e^{- 2 c_{1}} - e^{- 2 c_{1}} x^{2} + 1, y = - e^{- 2 c_{1}} - e^{- 2 c_{1}} x^{2} + 1

y = e^{- 2 c_{1}} - e^{- 2 c_{1}} x^{2} + 1, y = - e^{- 2 c_{1}} - e^{- 2 c_{1}} x^{2} + 1

y^{^{'}} = \frac{t y ^{2}}{t ^{2} + e}

y^{^{'}} = 1 + y + y^{2}

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

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

(2 + x) d y - y d x = 0