Question

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

Answer 1

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