Solve `x (dy)/(dx)sin(y/x)+x-ysin(y/x)=0` given `y(1)=pi/2`

Solve (dy)/(dx)=cos(x+y)-sin(x+y) .

(xe^(y/x)-ysin(y/x))dx+xsin(y/x)dy=0

Solve: x (dy)/(dx)- y-x tan . (y/x) . = 0

Solve: (dy)/(dx)+(y)/(x)=cos x+(sin x)/(x)

Solve (dy)/(dx)=(1+x^(2))/(y+sin y)

Solve (dy)/(dx)=(sin y+x)/(sin2y-x cos y)

Solve x (dy) / (dx) sin ((y) / (x)) + xy sin ((y) / (x)) = 0 given y (1) = (pi) / (2)

Show that the differential equation x(dy)/(dx)sin(y/x)+x-ysin(y/x)=0 is homogenous. Find the particular solution of this differential equation, given that x=1 when y=pi/2 .

Solve: (dy)/(dx)=-(x+y cos x)/(1+sin x)

Solve (dx )/(dy) +x/y= sin y