(a) Show that the solutionu(t) of u'= 1/(t^2+ e^u); u(t0)=u_0 exists and is unique for all t>=t0.(Can you prove the same conclusion for t > min {t0; 0} and explaine the answer.
(b) Show that limu(t) with t--> infty exists.
(a) Show that the solutionu(t) of u'= 1/(t^2+ e^u); u(t0)=u_0 exists and is unique for all t>=t0.(Can you prove the same conclusion for t > min {t0; 0} and explaine the answer.
(b) Show that limu(t) with t--> infty exists.