(dy}{dx}=\frac{2y)/x+(y^2)/x

Lösung

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

y = \frac{2 e ^{2 c_{1}} x ^{2}}{1 - e ^{2 c_{1}} x ^{2}}

Schritte zur Lösung

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

Solve separable ODE:

y = \frac{2 e ^{2 c_{1}} x ^{2}}{1 - e ^{2 c_{1}} x ^{2}}

y = \frac{2 e ^{2 c_{1}} x ^{2}}{1 - e ^{2 c_{1}} x ^{2}}

\frac{d P}{d t} = 1.1 P (1 - \frac{P}{5000})

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

y^{^{'}} + 16 x y = x

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

y^{^{'}} = 12 y - 15