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

  1. Jan 23, 2009 #1
    1. The problem statement, all variables and given/known data
    It's a modeling question, the question itself doesn't matter because i know how to do, but stuck on one of the equations

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

    3. 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

    how? why??/

  2. jcsd
  3. Jan 23, 2009 #2
    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.
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