Find the solution of the differential equation that satisfies the given initial condition.

Question

du/dt= (2t + sec^2(t))/(2u), u(0) = −4

Answer 1

du/dt = (2t + sec^2(t))/(2u)
2u du = (2t + sec^2(t)) dt
u^2 = t^2 + tan(t) + c

16 = 0+0+c

u^2 = t^2 + tan(t) + 16

Answer 2

again for this one do you mean it would be u= - sqrt(t^2+tan(t)+16) if so that is what i have but was just trying to confirm before entering it into the online homework system so i don't seem like an idiot if the professor checks to see how many attempts I've taken on the homework problems.

Answer 3

If you want an explicit function, then you are correct.