Solve the differential equation : `y sqrt(1-x^2)dy - sqrt(1+y^2)dx = 0`

Solve the Differential Equation : y sqrt(4-x^2) dy - sqrt (2+y^2) dx= 0

Solve the differential equation: dy=x(x^2-2y)dx

Solve the following differntial equations: sqrt(1+x^2)dy+sqrt(1+y^2)dx=0 .

Solve the differential equation (dy/dx) = (sqrt(1-y^2))/(sqrt(1-x^2))

Let a solution y = y(x) of the differential equation xsqrt(x^2-1) dy - y sqrt(y^2-1) dx=0 , satisfy y(2)= 2/sqrt 3

Solve the differential equation : x (1 + y^2) dx - y (1 + x^2) dy = 0 given that y = 0 when x = 1

Solve the differential equation : (x+y)dy-(y-x)dx=0 .

Solve the differential equation : (x-y)dy-(x+y)dx=0 .