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Homework Help: Is this DE nonlinear?

  1. Jan 15, 2009 #1
    Is this DE nonlinear????

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

    Determine the order and if this equation is Linear or Nonlinear.

    3(d4x/dt4) + 4(dx/dt) + 9x = 3cos(3t)

    The d4x is a forth order derivative. Sorry for the messiness.

    Ok, this is a 4th order DE. I think it is nonlinear because of the two products (multiplying 4 time the derivative and 4 times the other derivative).

    Also, the 3cos(3t) has no bearing on this because t is independent right? If the t was a y, that would cause nonlinearness.

    Am I right on all this?
     
  2. jcsd
  3. Jan 15, 2009 #2
    Re: Is this DE nonlinear????

    Define linear DE
     
  4. Jan 15, 2009 #3
    Re: Is this DE nonlinear????

    A linear differential equation is one in which the derivative has no function of itself (e^y, cosy, ln(y)). That is if I was differentiating with respect to y.
     
  5. Jan 15, 2009 #4
  6. Jan 15, 2009 #5
    Re: Is this DE nonlinear????

    Ok.. So my equation is Linear. But you cannot have, 3a*y'. This product will make it nonlinear.
     
  7. Jan 15, 2009 #6
    Re: Is this DE nonlinear????

    What's a?
     
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