1. anonymous

$\frac{ du }{ dt }=e ^{6u+8t}$ given that u(0)=8. So this is how I set it up $\int\limits_{}^{}e ^{-6u}du=\int\limits_{}^{}e ^{8t}dt$

2. anonymous

Is that right so far?

3. anonymous

yes looks right. so far.

4. anonymous

Okay, so this is what I got for my integration: $\frac{ -e ^{-6u} }{ 6 }=\frac{ e ^{8t} }{ 8 }+c$

5. anonymous

and then using that u(0)=8, I found that c=-0.125.

6. anonymous

I actually have already worked through this problem, but I got the wrong answer at the end so I'm trying to figure out where I'm going wrong

7. anonymous

so then I end up with $\frac{ -e ^{-6u} }{ 6 }=\frac{ e ^{8t} }{ 8 }-0.125$

8. anonymous

so then my final answer was u(t)=$\frac{ 1 }{ 6 }\ln(\frac{ 3 }{ 4 }e ^{8t}-\frac{ 3 }{ 4 })$

9. anonymous

but the book says that isn't the right answer

10. anonymous

hmm well i also got c same as u.. well what answer book says?

11. anonymous

well, it's actually webwork, so it just tells me that my answer is wrong, I'm not sure what the right answer is

12. anonymous

I'm thinking something must be wrong with the way I'm doing the algebra to rearrange it in terms of u(t)?

13. anonymous

well i am not sure but the way u solved question looks fine and the answer should be the one u got..

14. anonymous

hmmm. Okay. I'll ask the tutor at 8. Thanks anyway :)