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Is this DE linear?

  1. Mar 2, 2013 #1
    (y^2)'' + (y^2)' + y^2 = 0

    1) Is this DE linear?

    What if we substitute y^2 = h
    and solve for h
    y = sqrt(h)

    2) Would that be valid?
    3) Would that be considered a somewhat trivial type of linearization?
     
  2. jcsd
  3. Mar 2, 2013 #2

    rbj

    User Avatar

    if you make that substitution, it's linear.
     
  4. Mar 3, 2013 #3
    cocopuff,

    No, of course not. The dependent variable is "y" and y^2 is nonlinear.

    Yes.

    No, linear DE's are not classified as trivial linear or nontrivial linear DE's.

    Ratch
     
  5. Mar 3, 2013 #4

    pasmith

    User Avatar
    Homework Helper

    Yes.

    If you want y to be real-valued, then you will need [itex]h(t) \geq 0[/itex] for all t. Unfortunately the general solution of that particular ODE is oscillatory with a decaying amplitude, so there will be intervals where [itex]h(t) < 0[/itex] unless [itex]h(t) = 0[/itex] for all t.
     
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