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Nonlinear 1o Order D.E.

  1. Aug 22, 2012 #1
    Hello!!

    I am taking a self study diff e course, and I have run into a problem with no one to ask for help.
    Here is the problem:

    d/dt [ h^3(t) + 3h(t)^2 + 3h(t) ] = q(t)

    h(t) is output.
    q(t) is input.

    is this Nonlinear First Order Differential Equation.
    But I could not expand to Taylor Series for linearization... :/

    I'm trying to find the transfer function.

    Thanks!
     
  2. jcsd
  3. Aug 22, 2012 #2

    HallsofIvy

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    It should be basic Calculus that
    [tex]\frac{d}{dx}(h^3+ 3h^2+ 3h)= q(t)[/tex]
    [tex] 3h^2\frac{dh}{dt}+ 6h\frac{dh}{dt}+ 3\frac{dh}{dt}= (3h^2+ 6h+ 3)\frac{dh}{dt}= q(t)[/tex]
    Now what is the linearization of that?
     
  4. Aug 28, 2012 #3
    Maybe this will help:

    h3 + 3 h2 + 3h = (h +1)3 -1
     
  5. Aug 29, 2012 #4
    Hi !
    Why not imtegrate it first ?
     

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  6. Mar 30, 2013 #5
    Yeah! Thank you very much!
    :)
     
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