Find the general solution of the differential equations y log y dx x dy = 0

Explanation

Given, `y log y dx-xdy=0`
`implies y log ydx=xdyimplies (1)/(x)dx=(1)/(y log y)dy`
`implies int(1)/(x)dx=int(1)/(y logy)dy`
Let `logy=timplies (1)/(y)dy=dt`
`:. Int(1)/(x)dx=int(1)/(t)dt`
`implies log|x|=log|t|-log|C|`
`implies log|xC|=log|logy|`
`gt Cx=logyimplies y=e^(Cx)`
which is the required general solution.