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Differential equation help solving homogeneous equations

  1. Jan 23, 2010 #1
    1. The problem statement, all variables and given/known data

    Find a general solution if possible, otherwise find a relation that defines the solutions implicity.

    xy'-y=x tan(y/x)

    2. Relevant equations



    3. The attempt at a solution

    y'-(y/x) = tan(y/x)

    v = y/x ; y = xv ; y' = xv' + v

    xv' + v = tan(v) + v

    xv' = tan(v)

    I got stuck there i'm not exactly sure how to integrate [tan(v)/x] to get v
    and once i get v i'm not sure what to do to get y.

    from using mathmatica command DSolve[xy'[x]-y[x]==xTan[y[x]/x],y[x],x] i got an answer of:

    y[x] = x*(ArcSin[(e^c)*x])

    Any help will be much appreciated!
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jan 23, 2010 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Don't try to integrate tan(v)/x. You've got x*dv/dx=tan(v). Separate the variables. dv/tan(v)=dx/x. Integrate both sides.
     
  4. Jan 23, 2010 #3
    thanks! i forgot all about separating variables! it was so much easier once i did that. i ended up getting the answer, thanks again!
     
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