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Differential Equation Root of Pt (aka xy)

  1. Jun 14, 2010 #1
    1. The problem statement, all variables and given/known data
    dP/dt=root of (Pt)

    2. Relevant equations

    3. The attempt at a solution
    Well, I figure that the integrating factor is 1, since there is no P(x) value, so it's a matter of finding the integral of root(Pt). I can't solve this because the only method I know is substitution, and it doesn't work on this equation.

    Thanks guys
  2. jcsd
  3. Jun 14, 2010 #2


    Staff: Mentor

    this equation is separable. Write sqrt(Pt) as P1/2t1/2.
  4. Jun 14, 2010 #3
    I see that, I guess I'm just confused by finding the integral of two variables. If I substitute u for Pt, and du=(t)dP/dt + P dt...

    will that work?
  5. Jun 14, 2010 #4


    Staff: Mentor

    You don't need to do a substitution and you aren't going to have any integrals with two variables.

    [tex]\frac{dP}{dt} = \sqrt{Pt} = P^{1/2}t^{1/2}[/tex]

    Separate to get the following.
    [tex]\frac{dP}{P^{1/2}} = t^{1/2} dt[/tex]

    Now integrate.
  6. Jun 14, 2010 #5
    shesh you're right, how silly of me.

    THanks a lot Mark!
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