(dy)/(dx)=(1-y^2)

Lösung

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

y = - \frac{e ^{2 x + 2 c_{1}}}{1 - e ^{2 (x + c_{1})}} - \frac{1}{1 - e ^{2 (x + c_{1})}}

Schritte zur Lösung

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

Solve separable ODE:

y = - \frac{e ^{2 x + 2 c_{1}}}{1 - e ^{2 (x + c_{1})}} - \frac{1}{1 - e ^{2 (x + c_{1})}}

y = - \frac{e ^{2 x + 2 c_{1}}}{1 - e ^{2 (x + c_{1})}} - \frac{1}{1 - e ^{2 (x + c_{1})}}

\frac{y - 1}{y ^{2}} d y = \frac{1 + x}{x ^{2}} d x

y^{^{'}} = 11 - y

\frac{y ^{2}}{x} \cdot y^{^{'}} = 1 + x^{2}

x^{^{'}} = t (1 - t) x

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