(dy)/(dx)=(2x^2)/(y+1)

Lösung

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

y = \frac{- 6 + 36 - 12 ( - c _{1} - 4 x ^{3} )}{6}, y = \frac{- 6 - 36 - 12 ( - c _{1} - 4 x ^{3} )}{6}

Schritte zur Lösung

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

Solve separable ODE:

y = \frac{- 6 + 36 - 12 ( - c _{1} - 4 x ^{3} )}{6}, y = \frac{- 6 - 36 - 12 ( - c _{1} - 4 x ^{3} )}{6}

y = \frac{- 6 + 36 - 12 ( - c _{1} - 4 x ^{3} )}{6}, y = \frac{- 6 - 36 - 12 ( - c _{1} - 4 x ^{3} )}{6}

y^{^{'}} - y = - 1

y^{^{'}} = \frac{x + 4}{y ^{2}}

y^{^{'}} = \frac{4 x y}{x ^{2} + 1}

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

\frac{d y}{d x} = \frac{1 + x}{y}