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1st order differential eqn raised to power of 1.7

  1. Sep 14, 2009 #1
    1. The problem statement, all variables and given/known data
    This is the eqn I need to solve:
    (dy/dx)^1.7 = c

    2. Relevant equations



    3. The attempt at a solution
    1) 1.7ln(dy/dx) = c [since 'c' is an arbitrary constant, i'm writing ln(c) as 'c' itself]

    2)ln(dy/dx) = c/1.7

    3)dy/dx = e^(c/1.7)

    4)y = xe^(c/1.7)

    Now, the above solution says that y is a linear function of x. The solution is similar to what we obtain for "dy/dx = c", i.e. another linear solution. So I'm beginning to wonder whether what I did was correct. Can anyone help?
     
  2. jcsd
  3. Sep 14, 2009 #2
    You could just take the 1.7th root of the equation to get this

    [tex]\frac{dy}{dx}=c^{\frac{1}{1.7}}[/tex]

    [tex]\frac{dy}{dx}=c'[/tex]

    Where c' is just another constant.

    So in other words, it is just a linear function.
     
  4. Sep 14, 2009 #3
    Thanks for the reply Prologue. So if this is a linear function too, then what exactly is the difference between the solution for "dy/dx = c" and "(dy/dx)^1.7 = c" besides the actual numerical value of dy/dx?
     
  5. Sep 14, 2009 #4
    In differential equation terms...nothing. They have the same solution,

    y = (arbitrary constant)x + (arbitrary constant)
     
  6. Sep 14, 2009 #5
    Cool.. Thanks again...
     
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