(dy}{dx}=\frac{y^{1/2}ln(x))/x

解

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

y = \frac{ln ^{4} ( x )}{16} + \frac{c _{1} ln ^{2} ( x )}{4} + \frac{c _{1}^{2}}{4}

解答ステップ

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

分離可能 ODE を解く:

y = \frac{ln ^{4} ( x )}{16} + \frac{c _{1} ln ^{2} ( x )}{4} + \frac{c _{1}^{2}}{4}

y = \frac{ln ^{4} ( x )}{16} + \frac{c _{1} ln ^{2} ( x )}{4} + \frac{c _{1}^{2}}{4}