(dy)/(dx)=-(y(1-x))/(x(1-y))

解答

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

y = - W (- \frac{1}{e ^{- x - c_{1}} x})

求解步骤

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

求解可分离方程:

y = - W (- \frac{1}{e ^{- x - c_{1}} x})

y = - W (- \frac{1}{e ^{- x - c_{1}} x})

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

\frac{d y}{d x} = \frac{2}{5 x y} x, y > 0

y^{^{'}} + 2 x y - x = 0

\frac{d y}{d t} = 2 c - y

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