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How to solve this equation

  1. Sep 18, 2007 #1
    1. The problem statement, all variables and given/known data

    A certain population has a growth rate that satisfies the differential equation:

    [tex]\frac{dy}{dt}[/tex]=[0.5+Sin(t)][tex]\frac{y}{5}[/tex]

    If y(0)=1 find the time [tex]\tau[/tex] that the population has doubled.

    2. Relevant equations



    3. The attempt at a solution

    This is a simple separable differential equation but when I try to solve for t when the population has doubled I get the following equation, and I can't figure out how to solve for t. I know that the equation is correct because my calculator solved it and gave the correct answer. I'm just trying to figure out where to go from here:

    2Cos(t)-t=10Ln(2)-2

    Thanks

    Sorry about my poor use of latex
     
  2. jcsd
  3. Sep 18, 2007 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Your calculator omitted an integration constant. You'll have to have talk with it. Seriously, when you integrate something it introduces an arbitrary constant, remember?
     
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