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Obtaining General Solution of ODE

  1. Nov 1, 2016 #1
    1. The problem statement, all variables and given/known data
    So they want me to obtain the general solution for this ODE.
    Screen Shot 2016-11-01 at 12.00.43.png

    2. Relevant equations
    I have managed to turn it into d^2y/dx^2=(y/x)^2.

    3. The attempt at a solution
    My question is, can I simply make d^2y/dx^2 into (dy/dx)^2, cancel the power of 2 from both sides of the equation and then integrate it normally?

    If not, why?
     
  2. jcsd
  3. Nov 1, 2016 #2

    rock.freak667

    User Avatar
    Homework Helper

    I believe you can however, just make sure that you re-write it as dy/dx = +/- y/x


    Also note the distinction that d^2y/dx^2 = d/dx(dy/dx) i.e. differentiating dy/dx wrt x and (dy/dx)*(dy/dx) = (dy/dx)^2.
     
  4. Nov 1, 2016 #3

    Mark44

    Staff: Mentor

    In other words, solve dy/dx = y/x as well as dy/dx = -y/x.
     
  5. Nov 1, 2016 #4
    Thanks guys!
     
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