ln(x)=xyy^'

解答

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

y = ln^{2} (x) + c_{1}, y = - ln^{2} (x) + c_{1}

求解步骤

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

求解可分离方程:

y = ln^{2} (x) + c_{1}, y = - ln^{2} (x) + c_{1}

y = ln^{2} (x) + c_{1}, y = - ln^{2} (x) + c_{1}

\frac{2 ( y - 2 x \frac{d y}{d x} )}{3 y ^{3}} = 0

\frac{d y}{d x} + 2 y + 3 = 0

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

\frac{d y}{d x} = 50 (y - 10000)

x \cdot y^{^{'}} = 4 y