The solution of dydx=y(xlogy-y)x(ylogx-x) is
xy=cyx
xy=c
(xy)x=c
None of these
Explanation for the correct option:
Find the solution of given differential equation
Given differential equation: dydx=y(xlogy-y)x(ylogx-x)
⇒x(ylogx−x)dydx=y(xlogy−y)⇒logx−xydydx=logy−yx⇒yx+logxdydx=logy+xydydx⇒ddx(ylogx)=ddx(xlogy)⇒ylogx=xlogy+logc⇒logxy=logyx+logc⇒xy=cyx
Hence, option (A) is the correct answer.