x^2y^2+(1+y^2)y^'=0

Lösung

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

y = \frac{3 c _{1} - x ^{3} + ( - 3 c _{1} + x ^{3} ) ^{2} + 36}{6}, y = \frac{3 c _{1} - x ^{3} - ( - 3 c _{1} + x ^{3} ) ^{2} + 36}{6}

Schritte zur Lösung

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

Solve separable ODE:

y = \frac{3 c _{1} - x ^{3} + ( - 3 c _{1} + x ^{3} ) ^{2} + 36}{6}, y = \frac{3 c _{1} - x ^{3} - ( - 3 c _{1} + x ^{3} ) ^{2} + 36}{6}

y = \frac{3 c _{1} - x ^{3} + ( - 3 c _{1} + x ^{3} ) ^{2} + 36}{6}, y = \frac{3 c _{1} - x ^{3} - ( - 3 c _{1} + x ^{3} ) ^{2} + 36}{6}

(x^{2} - 4) y^{^{'}} - 4 y = 0

\frac{d y}{d x} = x y^{2} + x

\frac{d y}{d x} = - 9 x^{2} y

y^{4} y^{^{'}} - 3 y^{5} = 0

\frac{d x}{d t} = 8 x t^{3}