Case Study-III
An equation involving derivatives of the dependent variable with respect to the independent variables is called a differential equation. A differential equation of the form ‌

dy

dx

=F(x,y) is said to be homogeneous if F(x,y) is a homogeneous function of degree zero, whereas a function F(x,y) is a homogenous function of degree n if F(λx,λy)=λnF(x,y). To solve a homogeneous differential equation of the type ‌

dy

dx

=F(x,y)= g(‌

y

x

), we make the substitution y=vx and then separate the variables. Based on the above, answer the following questions :
(I) Show that (x2−y2)dx+2xydy=0 is a differential equation of the type ‌

dy

dx

=g(‌

y

x

).
(II) Solve the above equation to find its general solution.