Given the problem du/dt = e^(6u+2t)
i cant seem to separate the two variables
i tried using the natural logarithm of both sides but only got
$\displaystyle ln(du)=(6u+2t)*ln(dt)$
edit:
using the index law i was able to get it down to
$\displaystyle \dfrac{e^-^6^u}{-6} = \dfrac{e^2^t}{2} + C $
i was given the initial conditions of u(0) = 12
and got $\displaystyle C = \dfrac{-e^-^7^2}{6}-\dfrac{1}{2}$
after putting it back in the equation and putting it in terms of u
i got to the end and got $\displaystyle u = \dfrac{ln((-3e^2^t)+(e^-^7^2)-3)}{-6} $
but seems to be the wrong answer still.