posted by mike .
solve the initial value problem by seperation of variables du/dt=2t+sec2t/2u, u(0)=-5
The following equation is separable (please check this is the same as your question after adding appropriate parentheses):
du/dt = (2t+sec(2t)) / (2u)
transpose terms to get:
(2u)du = (2t+sec(2t))dt
Integrate both sides (do not forget the integration constant) and substitute u(0)=-5 (i.e. u(t)=-5, when t=0) to evaluate the integration constant.
Post your answer for a check if you wish.