The given difierential equation is:
Thus, F(x, y) is a homogenous function of degree zero.
Therefore, the given differential equation is a homogeneous differential equation.
To solve it we make the substitution
y = vx …(2)
Differentiating equation (2). with respect to x, we get
dy/dx = v + x dv/dx .....(3)
Substituting the value of y and dy/dx in equation (1)
we get,
which is the general solution of the differential equation (1).
