# Math Help - Separable Differential Equation Question

1. ## Separable Differential Equation Question

Question:
Solve the separable differential equation for
Use the following initial condition: .
?

My work:
(Attached)

Any help would be greatly appreciated!

2. Originally Posted by s3a
Question:

Solve the separable differential equation for

Use the following initial condition: .
?

My work:
(Attached)Any help would be greatly appreciated!
$\frac{du}{dt} = e^{4u+8t} = e^{4u}\times e^{8t},u(0)=-6$

Therefore

$e^{-4u}~du= e^{8t}~dt$

$\frac{-1}{4}e^{-4u}= \frac{1}{8}e^{8t}+C$

$e^{-4u}= \frac{-1}{2}e^{8t}+C$

$-4u= \ln(\frac{-1}{2}e^{8t}+C)$

$u= \frac{-1}{4}\ln(\frac{-1}{2}e^{8t}+C)$