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Constant or Variable Coefficients?

  1. Apr 21, 2007 #1

    ssb

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    1. The problem statement, all variables and given/known data

    [tex] ty' + y = \sin(t) [/tex]

    state the following:

    Order of the DE
    1st 2nd 3rd or n/a

    Linear
    Nonlinear
    Not Applicable

    Homogeneous
    Nonhomogeneous
    Not Applicable


    Constant Coefficients
    Variable Coefficients
    Not Applicable


    2. The attempt at a solution

    1st,
    Linear,
    Nonhomogeneous

    but I dont know how to distinguish between constant or variable coefficients. Is there an easy way to remember the rule here? Thanks
     
  2. jcsd
  3. Apr 21, 2007 #2

    ssb

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    im pretty sure its variable because there are some y's that vary as t changes.
    If this is accurate just let me know.

    Also if there is a differential equation

    [tex]y'' + y^2 = 0[/tex]

    does the fact that the y^2 make it non linear? Im hearing different arguments both ways here. Thanks! Im pretty sure that the y^2 makes it non linear by the way.
     
    Last edited: Apr 21, 2007
  4. Apr 21, 2007 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    The coefficient of y' is t. Is that a constant or will it vary as t varies?

    As for your second question, I don't know how you could "hear arguments both ways"! You might do well to ignore, in the future, those who "argue" that this is linear. y uis the "dependent variable" and y2 is definitely a non-linear function of y! This is, without argument, a "non-linear" differential equation!
     
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