(dy)/(dx)=\sqrt[3]{x(y-1)},y(0)=1

Lösung

\frac{d y}{d x} = 3 x (y - 1), y (0) = 1

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

Schritte zur Lösung

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

Solve separable ODE:

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

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

y^{^{'}} = \frac{21 x}{y}

\frac{d t}{d y} = (2 t y^{2})

\frac{d y}{d x} = - 7 x y^{3}

(x^{2} + 4) y^{^{'}} + x y = 9 x

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