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Linearity of differential equation

  1. Dec 14, 2013 #1
    Friends I have one doubt

    Below given equation is linear or non linear


  2. jcsd
  3. Dec 14, 2013 #2


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    It's non-linear, because of the cos x coefficient. Compare it to the ODE for a pendulum, which is non-linear, but can be linearized if small deflections are assumed.
  4. Dec 14, 2013 #3
    Mathematically,the equation you wrote is considered a linear ordinary differential equation with non-constant coefficients. It is considered linear if the homogeneous part is linear with respect to the dependent variable (in this case y).
  5. Dec 14, 2013 #4
    But what about -5 term
  6. Dec 14, 2013 #5
    That's not included in the homogeneous part.
  7. Dec 14, 2013 #6
    Linear, because all exponents of y aren't different of +1.
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