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Seperable Differential equation

  1. Apr 12, 2013 #1
    dm/ds=m ; m(1)=7

    when i find the diff eq

    ∫dm/m=∫ds

    ln|m|+c1=s+c2 ; k=c2-c1

    ln|m|=s+k
    e ^ both sides

    m(s)=e^(s+k) ; m(1)=7

    m(1)=e^(1)*e^(k)=7
    i am stuck here. not sure how to proceed please help.
     
  2. jcsd
  3. Apr 13, 2013 #2
    What are you trying to figure out with your initial condition?

    Can you solve this equation using another technique?
     
  4. Apr 13, 2013 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    There is really no need to write both c1 and c2. It's perfectly proper to immediately combine the two "constants of integration" to write ln|m|= s+ k.

    ln|m|=s+k
    e ^ both sides

    m(s)=e^(s+k) ; m(1)=7

    m(1)=e^(1)*e^(k)=7
    i am stuck here. not sure how to proceed please help.[/QUOTE]
    So e^k= 7e^{-1}.

    e^(s+k)= e^k e^s so m(s)= 7e^{-1}e^k or m(s)= 7e^(k-1).
     
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