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Linearity in Differential Equations

  1. Mar 26, 2012 #1
    1. The problem statement, all variables and given/known data

    Is the following differential equation linear:

    [itex]yy' + 2 = 0[/itex]

    3. The attempt at a solution

    I have the definition of linear as being [itex]a_0 (t) y^{(n)} + a_1(t) y^{n-1} + a_2 (t) y^{n-2} ... = 0[/itex]. Now, presumably y is a function of t. Thus, I could define [itex]y = a_0 (t) [/itex] and let n=1. Thus I would satisfy my definition of linearity in differential equations. Thus, the differential equation is linear.

    Is it not so?
     
  2. jcsd
  3. Mar 26, 2012 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    No, [itex]a_0(t)[/itex] has to be a known function of t, not y or anything involving y. This equation is non-linear because you have a product of things "involving" the dependent variable y.
     
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