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

Lösung

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

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

Schritte zur Lösung

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

Solve separable ODE:

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

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

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

\frac{d y}{d x} = - \frac{( 2 x - 1 )}{( 3 y + 7 )}

2 x^{2} y + 3 x y^{^{'}} - (2 x^{2} - 1) y = 0

x^{2} y^{2} + 3 x y^{^{'}} = 0

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