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Rearranging separable equations

  1. Feb 3, 2013 #1
    I'm having difficulty with the question in the pic provided. (http://i.imgur.com/Fg7CHoY.png). Basically the equation im given is

    dy/dx = (y-4x)/(x-y)​

    and it walks through the steps needed to solve it, however, im supposed to show how to arrive at each step given. I've gotten part a, where it asks to show that the above equation can be written as

    dy/dx = (y/x - 4)/(1-y/x)​

    and, introducing v=y/x, rewrite dy/dx in terms of v, x, and dv/dx. What I get for part b is

    dy/dx = d(xv)/dx = x(dv/dx)​

    however, on part c, it looks like I'm supposed to get

    dy/dx = v+x(dv/dx)​

    I'm not sure where the additional v term comes from. If anyone could help me out, i would really appreciate it!
     
  2. jcsd
  3. Feb 3, 2013 #2

    haruspex

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    It's just the product rule. How do you differentiate f(x)g(x)?
     
  4. Feb 3, 2013 #3
    I cant believe it was that simple - I had been staring at it for hours. Thank you!
     
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