(dy)/(dx)=(3x^2)/(1-2y)

Lösung

\frac{d y}{d x} = \frac{3 x ^{2}}{1 - 2 y}

y = - \frac{- 1 + 1 + 4 ( - c _{1} - x ^{3} )}{2}, y = - \frac{- 1 - 1 + 4 ( - c _{1} - x ^{3} )}{2}

Schritte zur Lösung

\frac{d y}{d x} = \frac{3 x ^{2}}{1 - 2 y}

Solve separable ODE:

y = - \frac{- 1 + 1 + 4 ( - c _{1} - x ^{3} )}{2}, y = - \frac{- 1 - 1 + 4 ( - c _{1} - x ^{3} )}{2}

y = - \frac{- 1 + 1 + 4 ( - c _{1} - x ^{3} )}{2}, y = - \frac{- 1 - 1 + 4 ( - c _{1} - x ^{3} )}{2}

x^{2} y^{^{'}} = y^{2}

y^{^{'}} = \frac{cos ^{2} ( x )}{y}

x^{2} y^{^{'}} + \frac{1}{y ^{2}} = 0

y^{2} (x - 3) d x - x^{3} d y = 0

\frac{d y}{d t} = \frac{y + 3}{1 - y}