Find the particular solution.(x²-y²)dx+2xy dy=0.y=1,when x=1

Its a homogenous differential equation of the first order and degree.Find an expression for dy/dx.Substitute y=ax, and substitute everything, taking a as a function of x. It should convert into a variable seperable equation and can then be solved easily.

Divide through out by x^2 , then it will be in the form of a homogeneous diff. Eqn = dy/dx=( u^2)-1 / 2uWhere u= y/x.Now proceed as usual .Also dy/dx= u+ du/dx.du/dx= (u^2 - 1 / 2u )-u.Solve and continue.Hope it helps😃