sqrt(x-x^2)dy-xydx=0

解答

x - x^{2} d y - x y d x = 0

y = e^{- x (- x + 1) + \frac{1}{2} a r c s i n (2 x - 1) + c_{1}}

求解步骤

x - x^{2} d y - x y d x = 0

求解可分离方程:

y = e^{- x (- x + 1) + \frac{1}{2} a r c s i n (2 x - 1) + c_{1}}

y = e^{- x (- x + 1) + \frac{1}{2} a r c s i n (2 x - 1) + c_{1}}

\frac{d y}{d x} = \frac{3 x y}{( ln ( y ) ) ^{4}}

y^{^{'}} = \frac{2 y}{5 x}

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

\frac{d v}{d t} = 14 - 1.4 v

\frac{d y}{d x} = 6 x^{2} y, y > 0