`xdy/dxsin(y/x)+x-y*sin(y/x)=0`

Solve : {xcos(y/x)+ysin(y/x)}ydx={ysin(y/x)-xcos(y/x)}xdy

Solve the following differential equations y{x cos (y/x)+y sin (y/x)}dx- x{ y sin (y/x)-x cos (y/x)}dy=0 .

xdy/dx*tan(y/x)=ytan(y/x)-x , y(1/2)=pi/6 then the area bounded by x=0 , x=1/sqrt2 , y=y(x)

[x cos (y / x) + y sin (y / x)] y- [y sin (y / x) -x cos (y / x)] x (dy) / (dx) = 0

Solve {x cos((y)/(x))+y sin((y)/(x))}ydx={y sin((y)/(x))-x cos((y)/(x))}xdy

Show that the given differential equation is homogeneous and solve each of them.{x cos((y)/(x))+y sin((y)/(x))}ydx={y sin((y)/(x))-cos((y)/(x))}xdy

The general solution of the differential equation x.cos(y/x)(ydx+xdy)=y sin(y/x)(xdy-ydx) is (A) xy=c sec((x)/(y)) (B) y=xc sec((x)/(y)) (C) xy=c sec((y)/(x)) (D) None of these

Show that the differential equation: (xcos(y/x))(ydx+xdy)=(ysin(y/x))(xdy-ydx) is homogenous and solve it.

Prove that sin x* sin y*sin(x - y) + sin y *sin z*sin(y- z) + sin z *sin x sin(z - x) + sin(x - y) *sin(y - z)*sin(z -x) = 0 .