[" (ii) "(x cos(y)/(x)+y sin(y)/(x))ydx],[=(y sin(y)/(x)-x cos(y)/(x))xdy]

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

{x cos (y/x)+y sin (y/x)} y d x={y sin (y/x)-(x) cos (y/x)} x d y

{ xcos ((y)/(x)) + y sin ((y)/(x))} y dx = { y sin ((y)/(x)) - x cos ((y)/(x))}x dy

{ xcos ((y)/(x)) + y sin ((y)/(x))} y dx = { y sin ((y)/(x)) - x cos ((y)/(x))}x dy

Obtain the particular solution of the differential equation: { x cos ((y)/( x)) + y sin ((y)/( x))} ydx= { y sin ((y)/( x) ) - x cos ((y)/( x))}xdy where : x=2 when y= (pi)/(2) .