Solve the differential equation: `(xcos(y/x)+ysin(y/x))y-(ysin(y/x)-xcos(y/x))xdy/dx=0`.

Solve the differential equation xdy/dx+y=1/x^2 .

Solve the differential equation: [xsin^2(y/x)-y]dx+x dy=0 .

Solve the differential equation (x d y-y d x) y sin (y/x)=(y d x+x d y) x cos (y/x)

Solve the linear differential equation xdy/dx-y=(x-1)e^x

solve the differential equation (x^2+x y) d y=(x^2+y^2) d x

solve the differential equation (x^2-y^2) d x+2 x y d y=0

Solve the differential equation (tan ^-1 y-x) d y=(1+y^2) d x

Solve the following differential equations (dy)/(dx) + 2y = sin x

Solve the following differential equations (x + y)(dy)/(dx) = 1

The order of the differential equation (x/y) (d^2y)/(dx^2)+((xdy/dx-y)/x^2)dy/dx=0 is______