I am finding an asymptotic solution for the following ODE:

(eq1) dy/dt = yp [1 + log-a(2 + y2)] with p > 1, a > 0, y(0) = y0 > 0 .

We already know the solution of the following equation

(eq2) dy/dt = yp with p > 1, y(0) = y0 > 0

can solved by taking v = y1-p ==> y(t) = ((1-p)t + c)(-1/(p-1)) tends to +infinity as t -> T0 .

A question concerns with the solution of (eq1) that: u(t) ~~> ? as u(t) --> + infinity ( or t --> T1)
Should it be asymptotic as the solution of (eq2)?

Thank you anyone who can help to solve this problem!