Question

Find the solution of the differential equation that satisfies the given initial condition.
du/dt= (2t + sec^2(t))/(2u), u(0) = −4

Answers

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

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