(xy^2+x)dx+(x^2y-y)dy=0

Lösung

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

y = \frac{c _{1} - x ^{2} + 1}{x ^{2} - 1}, y = - \frac{c _{1} - x ^{2} + 1}{x ^{2} - 1}

Schritte zur Lösung

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

Solve separable ODE:

y = \frac{c _{1} - x ^{2} + 1}{x ^{2} - 1}, y = - \frac{c _{1} - x ^{2} + 1}{x ^{2} - 1}

y = \frac{c _{1} - x ^{2} + 1}{x ^{2} - 1}, y = - \frac{c _{1} - x ^{2} + 1}{x ^{2} - 1}

y^{^{'}} = - (1 - y) (2 - y)

y^{^{'}} = - \frac{1}{3} y^{2}

\frac{d y}{d x} = 60 y x^{9}

y^{^{'}} - 3 e^{5 x - 2 y} = 0

y^{^{'}} = - 9 x^{2} y