(dy)/(dx)=-((2xy+y^2+1))/(x^2+2xy)

解

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

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

解答ステップ

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

完全 ODE を解く:

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

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