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Determining Which Variable Is Independent

  1. Jan 23, 2014 #1

    I have a question with regards to solving problems that require knowledge of which variable is dependent and which is independent. Suppose I am presented with the differential equation [itex]x^5 y^{(4)} - x^3 y'' + 6y = 0[/itex]; for this differential equation I am asked to determine if it is linear or not. My question does not pertain to linearity, but is, how do I know which variable is the dependent? Is my knowing this solely due to the fact that the equation contains y and its derivatives, or does this not imply that y is the dependent variable?
  2. jcsd
  3. Jan 23, 2014 #2


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    If there are derivatives of y then it must be dependent on some variable; otherwise what are you differentiating with respect to?

    Often the writers are a bit glib in specifying the variable; for example your equation could have x be some arbitrary parameter and y be a function of t, which would change the solutions that you get. Unless specified though if something that looks like a variable (either x or t) appears in the equation then that is typically intended to be the independent variable.
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