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

Lösung

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

5 \frac{d Q}{d t} + \frac{1}{0.05} Q = 80

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

y^{^{'}} = sin (t) y

y^{^{'}} = - \frac{3}{7} x^{6} y^{4}

\frac{d y}{d x} = 4 x y - 18 x^{2} y