Solve : `(dy)/(dx)=(y(xcos""(y)/(x)+ysin""(y)/(x)))/(x(ysin""(y)/(x)-xcos""(y)/(x)))`

x(dy)/(dx)=y-xcos^(2)(y/x)

(x+ycos""(y)/(x))dx=xcos""(y)/(x)dy

(ysin""(y)/(x)-xcos""(y)/(x))xdy=(xcos""(y)/(x)+ysin""(y)/(x))ydx

Solve: y-x(dy)/(dx)=x+y(dy)/(dx)

Solve : (xdy-ydx)ysin""(y)/(x)=(ydx+xdy)xcos""(y)/(x) .

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

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

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

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