solve `(xdx+ydy)/(xdy - ydx) =sqrt((a^2 - x^2 - y^2)/ (x^2 + y^2))`

x dy - y dx = sqrt(x^(2) + y^(2)) dx

y = sqrt(1 + x^(2)) : y' = (xy)/(1 + x^(2))

Solve [2sqrt(x y)-x]dy+ydx=0

Solve (x+y(dy)/(dx))/(y-x(dy)/(dx))=x^2+2y^2+(y^4)/(x^2)

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

Solve (dy)/(dx)+2y=cos x.

Solve (dy)/(dx) + x sin 2y = x^(3) cos^(2) y

If sqrt(1-x^(2)) + sqrt(1 -y^(2))= a(x-y) , then prove that (dy)/(dx)= sqrt((1-y^(2))/(1-x^(2))) . (Where |x| le 1, |y| le 1 )

y dx + x log ((y)/(x))dy - 2xdy = 0

Solve (dy)/(dx)=e^(x-y)+x^(2)e^(-y) .