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

Lösung

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

y = c_{1}^{3} x^{3} + 3 c_{1}^{2} x^{2} + 3 c_{1} x + 1

Schritte zur Lösung

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

Solve Bernoulli ODE:

y = c_{1}^{3} x^{3} + 3 c_{1}^{2} x^{2} + 3 c_{1} x + 1

y = c_{1}^{3} x^{3} + 3 c_{1}^{2} x^{2} + 3 c_{1} x + 1

\frac{d y}{d x} = \frac{4 ( 1 + x )}{x y}

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

y^{^{'}} = 6 y

y^{^{'}} + 2 e^{x + y} = 0

\frac{d y}{d x} = 3 y