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2 equations. How to find X°/X?

  1. Mar 17, 2015 #1
    1. The problem statement, all variables and given/known data
    I have two equations.

    1. b(N) = rN^k

    2. bN° = Y - X - C

    How can I find an expression for N°/N




    2. Relevant equations


    3. The attempt at a solution

    I am a little lost here since I dont know much about the properties of differential equations. So my attempts at solution has been to take the derivative of the first equation and call it N°, which I dont know if I am alloved to do. Then insert it into the second equation and solve it for N. It doesent seem to be right.
     
  2. jcsd
  3. Mar 17, 2015 #2

    Mark44

    Staff: Mentor

    What is N° supposed to mean?
    I read your explanation below, but I still don't understand what you mean.
    Why not call it b'(N)? Differentiation both sides with respect to N would give b'(N) = rkNk - 1, but I don't see that doing this is helpful.

    Also, how do x and y tie in here? Your first equation involves N, and what appear to be constants, r and k.

    This is very confusing. What is the exact statement of the problem?
     
  4. Mar 17, 2015 #3

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Does your mysterious notation ##X^o## mean ##\dot{X} = dX(t)/dt##? If so, are you saying that you have
    [tex] \frac{d}{dt} \left( r N^k \right) = Y- X - C?[/tex]
    Are ##r,k## constants? Are ##N, Y, X,C## functions of ##t##? And, if ##X^o## does mean ##dX/dt##, where in your equations is there anything that tells you about ##dX/dt##?

    Please try to submit complete and readable questions, using standard notation.
     
  5. Mar 18, 2015 #4
    The question is from a paper.

    They write:

    If we substitute the formula for R&D cost from equation 6.36 into the resource constraint 6.23 we get:

    upload_2015-3-18_15-55-54.png


    6.36

    upload_2015-3-18_15-56-38.png
    6.23
    upload_2015-3-18_15-57-7.png

    X and Y

    upload_2015-3-18_15-58-55.png


    I dont really expect an answer here because I still think my post is not good enough. And also I cant bes sure I have provided you with all the necessary information, but if what they have done is intuitive to any of you and that you understand what they did, I would very much appreciate an answer.
     

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