Solve the differential equation:

given that when

Given: (x² + 3xy + y²)dx – x²dy = 0

…(i)

Let y = vx

On differentiating, we get

Putting the value of in eq. (i), we get

Integrating both the sides, we get

Now, put back the value of

…(ii)

It is given that when x=1, y=0

⇒ -1 = C [∵ log (1) = 0]

Putting the value of C in eq. (ii), we get