(y^2)/x*y^'=1+x^2

Lösung

\frac{y ^{2}}{x} \cdot y^{^{'}} = 1 + x^{2}

y = 3 \frac{3 x ^{2}}{2} + \frac{3 x ^{4}}{4} + c_{1}

Schritte zur Lösung

\frac{y ^{2}}{x} \cdot y^{'} (x) = 1 + x^{2}

Solve separable ODE:

y = 3 \frac{3 x ^{2}}{2} + \frac{3 x ^{4}}{4} + c_{1}

y = 3 \frac{3 x ^{2}}{2} + \frac{3 x ^{4}}{4} + c_{1}

x^{^{'}} = t (1 - t) x

\frac{d y}{d x} = \frac{1}{( x y ) ^{2}}

\frac{d x}{d t} + \frac{x}{50} = 4

x^{5} (\frac{d y}{d x}) = 3 x^{2} 1 - y^{2}

x \frac{d y}{d x} = 1 - y^{2}