The solution of `xy.log((x)/(y))dx+{y^(2)-x^(2)log((x)/(y))}dy`=

Show that the differential equation xylog(y/x)dx+{y^(2)-x^(2)log(y/x)}dy=0 is homogeneous and solve it.

The solution of x log x (dy)/(dx) + y = 2/xlog x is

The solution of (x^2+xy)dy=(x^2+y^2)dx is (A) logx=log(x-y)+y/x+C (B) logx=2log(x-y)+y/x+C (C) logx=log(x-y)+x/y+C (D) none of these

The solution of ((dy)/(dx))^(2)+(2x+y)(dy)/(dx)+2xy=0, is (i) (y+x^(2)-c_(1))(x+log y+y^(2)+c_(2))( (ii) (y+x^(2)-c_(1))(x-log y-c_(2))( iii) (y+x^(2)-c_(1))(x+log y-c_(2))( iv) (y+x^(2)-c_(1))(3x+log y-c_(2))

The general solution of x((dy)/(dx))+(log x)y=x^(-(1)/(2)log x) is

log ((dy)/(dx)) =2x +3y

The solution of (dy)/(dx)=e^(x)(sin^(2)x+sin2x)/(y(2log y+1)) is

The solution of (dy)/(dx)+(y)/(x)=(1)/((1+log x+log y)^(2)) is given by