y^'=x^2y^2-y^2+x^2-1

Lösung

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

y = tan (\frac{x ^{3}}{3} - x + c_{1})

Schritte zur Lösung

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

Solve separable ODE:

y = tan (\frac{x ^{3}}{3} - x + c_{1})

y = tan (\frac{x ^{3}}{3} - x + c_{1})

x^{2} \frac{d y}{d x} = 5 y

\frac{d x}{d t} = 14 - 0.84 x

2 x + 4 y \frac{d y}{d x} - c = 0

\frac{d y}{d x} = (y + 5) (2 x + 1)

\frac{d y}{d x} = 0.32 y