xdy-ydx=(xy)^{1/2}dx

解

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

y = \frac{1}{4} x ln^{2} (x) + c_{1} x ln (x) + c_{1}^{2} x

解答ステップ

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

ベルヌーイ ODE を解く:

y = \frac{1}{4} x ln^{2} (x) + c_{1} x ln (x) + c_{1}^{2} x

y = \frac{1}{4} x ln^{2} (x) + c_{1} x ln (x) + c_{1}^{2} x