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It looks simple but

  1. Nov 17, 2011 #1
    I ended up with this PDE:

    du/dt + A*u² =C

    A and C are constants and U is only function of time.
    It looks simple but...
    Can someone help me?
    Thanks a lot in advance
  2. jcsd
  3. Nov 17, 2011 #2


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    It is a Riccati equation, and indeed it is slightly more tricky than you may initially think.
  4. Nov 17, 2011 #3
    Thank you so much!! That was a quick answer!
  5. Nov 17, 2011 #4


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    Can't you just separate variables ?
  6. Nov 18, 2011 #5
    @dextercioby. That would work to solve for a function of u (e.g. f(u) = ...) , but kaniello here is solving for the function u(t) that satisfies the ODE... a much tricker problem that satisfies the riccati equation.
  7. Nov 18, 2011 #6


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    [tex] \frac{du}{dt} = C-Au^2 \Rightarrow \int dt = \int\frac{du}{C-Au^2} \Rightarrow...[/tex]

  8. Nov 18, 2011 #7
    ..which would be
    tanh⁻1([itex]\sqrt{a/c}[/itex] / (a/c).
    I am currently studying the article from CompuChip and reference given there. Probably this is the solution that comes out from the Riccati equation setting q1=0, q0 and q2= const.
  9. Nov 18, 2011 #8


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    The Riccati equation is only "tricky" in the general case - for example when C in the OP's equation is replaced by something like [itex]Ct^n[/itex]

    As dextercioby said, this special case is straighforward to integrate.
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