On the Emden-Fowler equation u″(t)u(t) = c1 + c2u′(t)2 with c1 ≥ 0, c2 ≥ 0

In this article, we study the following initial value problem for the nonlinear equation u″u(t)=c1+c2u′2(t),c1≥0,c2≥0,u(0)=u0,u′(0)=u1.We are interested in properties of solutions of the above problem. We find the life-span, blow-up rate, blow-up constant and the regularity, null point, critical point, and asymptotic behavior at infinity of the solutions.