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Differential Equations - re-arrange?

  1. Oct 21, 2009 #1
    1. The problem statement, all variables and given/known data

    So i am to differentiate: x dx = y^2 dy

    3. The attempt at a solution

    Am i right in thinking that i just do a simple re-arrangement to get: dx/dy = y^2/x and then differentiate this?

    I am unfamiliar with having to differentiate when both x and y are present in the equation. Any help will be much appreciated.

    Dan
     
  2. jcsd
  3. Oct 21, 2009 #2

    Mark44

    Staff: Mentor

    Is the object to find d2y/dx2? If so, solve for dy/dx, and then differentiate implicitly. That is, you differentiate x and functions of x alone as you normally would, but differentiate y and functions of y alone as if they were (implicitly) functions of x. You need to use the chain rule to do this.

    For example, d/dx(y2) = 2y * dy/dx.
     
  4. Oct 21, 2009 #3

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Your problem statement is confusing. Do you really mean differentiate? And if so, with respect to which variable? Or are you trying to solve a differential equation by using separation of variables and integrating?
     
  5. Oct 21, 2009 #4
    The question literally says: Solve The Following - x dx = y^2 dy, appologies for been unclear, but that is the very problem i have with the question i do not understand what is being asked for. I thought that there was perhaps something obvious to do with the equation.....
     
  6. Oct 21, 2009 #5

    Mark44

    Staff: Mentor

    That's what we were looking for, the literal statement of the problem.

    By "solve" it means find the solutions of the differential equation. It did not say to differentiate something.

    Do you know of any techniques for solving differential equations?
     
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