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Find a particular solution that satisfies the intial condition

  1. Nov 24, 2009 #1
    1. The problem statement, all variables and given/known data
    2xy'-ln x2=0 y(1)=2


    2. Relevant equations



    3. The attempt at a solution
    2x(dy/dx)-ln x2=0

    I think I'm suppose to separate variables and then integrate next but I'm not sure.
     
  2. jcsd
  3. Nov 24, 2009 #2

    Mark44

    Staff: Mentor

    Yes, this is a separable differential equation.

    You should use the fact that ln(x2) = 2ln(x).

    2x*dy/dx = 2 ln(x)
    [tex]\Rightarrow~dy~=~ \frac{ln(x)}{x}dx [/tex]

    Now integrate both sides. Don't forget the constant of integration, which you will determine from your initial condition, y(1) = 2.
     
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