x^2(dy)/(dx)+2xy-y^3=0

Lösung

x^{2} \frac{d y}{d x} + 2 x y - y^{3} = 0

y = \frac{5 x}{2 + 5 c _{1} x ^{5}}, y = - \frac{5 x}{2 + 5 c _{1} x ^{5}}

Schritte zur Lösung

x^{2} \frac{d y}{d x} + 2 x y - y^{3} = 0

Solve Bernoulli ODE:

y = \frac{5 x}{2 + 5 c _{1} x ^{5}}, y = - \frac{5 x}{2 + 5 c _{1} x ^{5}}

y = \frac{5 x}{2 + 5 c _{1} x ^{5}}, y = - \frac{5 x}{2 + 5 c _{1} x ^{5}}

\frac{d}{d x} (\frac{10}{x ^{7}})

x \to 0 - lim (\frac{1}{3 x})

a re a y = 3 x, x = 3, y = 1

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

x \to \infty lim (2 x^{2} + 5)