# Math Help - separable equations

1. ## separable equations

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

$ln(du)=(6u+2t)*ln(dt)$

2. Use the index law $a^{m + n} = a^m a^n$ to simplify the exponential.

3. edit:
using the index law i was able to get it down to

$\dfrac{e^-^6^u}{-6} = \dfrac{e^2^t}{2} + C$

i was given the initial conditions of u(0) = 12

and got $C = \dfrac{-e^-^7^2}{6}-\dfrac{1}{2}$

after putting it back in the equation and putting it in terms of u

i got to the end and got $u = \dfrac{ln((-3e^2^t)+(e^-^7^2)-3)}{-6}$

but seems to be the wrong answer still.

4. You've lost a sign. That final "-3" in the numerator should be positive. I would recommend making the entire fraction negative rather than having the negative sign in the denominator although that is, of course, the same result.

5. o sweet, finally got it right. Thank you!