2sqrt(xy)(dy)/(dx)=1

解答

2 x y \frac{d y}{d x} = 1

y = 3 \frac{9 x}{4} + \frac{9 c _{1} x}{2} + \frac{9 c _{1}^{2}}{4}

求解步骤

2 x y \frac{d y}{d x} = 1

求解可分离方程:

y = 3 \frac{9 x}{4} + \frac{9 c _{1} x}{2} + \frac{9 c _{1}^{2}}{4}

y = 3 \frac{9 x}{4} + \frac{9 c _{1} x}{2} + \frac{9 c _{1}^{2}}{4}

2 x y y^{^{'}} - 2 x^{2} + 1 = 0

x y^{^{'}} - y ln (y) = 0

y^{^{'}} - 4 x y = 2 x

\frac{d y}{d x} = \frac{7 ( 1 + x )}{x y}

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