x^3(1-y^3)dx-3y^2x^3(ydx+xdy)=0

Lösung

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

y = 3 \frac{c _{1} + x ^{4}}{4 x ^{4}}

Schritte zur Lösung

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

Solve separable ODE:

y = 3 \frac{c _{1} + x ^{4}}{4 x ^{4}}

y = 3 \frac{c _{1} + x ^{4}}{4 x ^{4}}

y^{^{'}} = y (1 - \frac{y}{2})

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

y^{^{'}} = ∣ y ∣^{2}

x y^{^{'}} + y = 1 + y^{^{'}}

y^{^{'}} = \frac{7 x ^{2} - 1}{7 + 11 y}