Differential Equation (this should be simple, even for me, but )

[myusernameis]

Homework Statement

It's a modeling question, the question itself doesn't matter because i know how to do, but stuck on one of the equations

Homework Equations

Q'(t)=15- 3Q(x)/800, Q(0)=2,

The Attempt at a Solution

I'm stuck at e^(3t/800) *Q(t) = 9/109 *e^(3t/800) +c

but the answer's supposed to be
Q(t)=4000-3998e^(-3t/800)..

how? why??/

thanks

 

[phreak]

I don't understand what method you are trying to use. The typical method is: set all constants to zero, and solve this equation for Q. That is, Q'(t) + 3Q(t)/800 = 0. The answer is clearly e^(3t/800). Now multiply the entire equation by this number:

Q'(t)e^(3t/800) + 3e^(3t/800)Q(t)/800 = 15. But the stuff on the left is just (Q(t)e^(3t/800))' by the product rule. So integrate both sides, find the missing constants, and you're done.