calculus
posted by joseph .
solve the initial value problem by seperation of variables du/dt=2t+sec2t/2u, u(0)=5

I am guessing that you mean sec^2 and left out parentheses
du/dt=(2t+sec^2t)/2u, u(0)=5
2 u du = 2 t dt + sec^2 t dt
u^2 = t^2 + tan t + c
when t = 0, u = 5
25 = c
u^2 = t^2 + tan t + 25