8y^2(xdy+ydx)=ydx-xdy

解

8 y^{2} (x d y + y d x) = y d x - x d y

y = \frac{c _{1} + c _{1}^{2} + 32 x ^{2}}{16 x}, y = \frac{c _{1} - c _{1}^{2} + 32 x ^{2}}{16 x}

解答ステップ

8 y^{2} (x d y + y d x) = y d x - x d y

線形 ODE を解く:

y = \frac{c _{1} + c _{1}^{2} + 32 x ^{2}}{16 x}, y = \frac{c _{1} - c _{1}^{2} + 32 x ^{2}}{16 x}

y = \frac{c _{1} + c _{1}^{2} + 32 x ^{2}}{16 x}, y = \frac{c _{1} - c _{1}^{2} + 32 x ^{2}}{16 x}