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Differential equation initial value prob

  1. Sep 23, 2009 #1
    1. The problem statement, all variables and given/known data

    http://img16.imageshack.us/img16/1008/questionsh.th.jpg [Broken]

    2. Relevant equations



    3. The attempt at a solution

    My question is that should we divide each side by sin(t) first? Because I tried dividing it with sin(t) and then I have u(x) = exp(csc(x)), which is kind of hard to integrate.

    Reason why I divide it by sin(t) is to get the following factor

    y' + p(x)y = q(x)

    and u(x) = exp(integral of p(x) dx)

    please correct me steps ehre
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Sep 23, 2009 #2

    rock.freak667

    User Avatar
    Homework Helper

    yes divide by sin(t)



    [tex]\int \frac{cost}{sint} dt[/tex]

    notice that d/dt(sint)= cost ?
     
  4. Sep 23, 2009 #3
    This will be equal to:

    [tex]\int cot(t) dt[/tex]

    which is:

    [tex]{-(csc(t))}^2[/tex]

    and so u(x) is e^(csc(t))
     
  5. Sep 23, 2009 #4
    remember the formula for d/dx(ln x)

    d/dx(ln x)= x'/x

    separate cot into cos/sin.
     
    Last edited: Sep 23, 2009
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