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Differential equation what going on?

  1. Mar 18, 2009 #1
    Hi could someone explain why this result occurs when solving this differential equation.

    dx/dt= xt

    1/xdx/dt=t then intergrating both side we get with respect to dt we get,

    Inx=t^2/2 + c now this is the bit i don't understand why does the answer then become,


    I get really confused how the equation gets re-arranged into the above form after the intergration has occured. Any help please?

  2. jcsd
  3. Mar 18, 2009 #2
    You are just exponentiating both sides of the equation. But remember that exponential functions and log's are inverse functions so e^lnx=x
  4. Mar 18, 2009 #3
    Thanks but how come it is c*the e and then raised to the power of 2/t^2. Is that just a rule of exponentials?
    Please help doing my head in!!

  5. Mar 18, 2009 #4


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    Hi James! :smile:

    No, x = Cet2/2

    C is ec. :wink:
  6. Mar 18, 2009 #5
    Hey James
    dx/dt= xt
    dx/x = t·dt
    Ln(x) = (t^2)/2 + K
    x=e t2 /2 +K = e K · e t2 /2
    If we say that e^K = C then;
    x= C·e t2 /2

    I hope it helps
  7. Mar 18, 2009 #6
    Thanks all for your help got it now!! thanks again james : -)
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