Solve the differential equation:

We need to solve the given differential equation

{∵ λ⁰= 1}

So, F(x, y) is a homogeneous function of degree zero

⇒ It is a homogeneous differential equation

Let y = vx

Differentiating with respect to x:

Integrating both sides:

Let 1 – 2v – v² = t

⇒ (-2 – 2v) dv = dt

Now again put the value of t = 1 – 2v – v²:

{∵ log(ab) = log a + log b}

Hence, solution of the differential equation is

x² – 2xy – y² = c