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Basic differential Equation

  1. May 30, 2009 #1

    TG3

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    The problem statement, all variables and given/known data
    Show that y = x-(x^-1) is a solution for the differential equations:
    xy' +y = 2x

    The attempt at a solution
    Frankly, I haven't a clue how to start.

    If it weren't for the x in the xy' term this would be easy, since I could just integrate; unfortunately, I don't know how to separate the x's from the y's, and this is really a problem, because this is the first problem from the homework set. I re-read the textbook, but don't get it. Any suggestions for techniques to separate the variables?
     
  2. jcsd
  3. May 30, 2009 #2

    Nabeshin

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    Science Advisor

    The problem isn't asking you to solve the differential equation, merely to verify that the solution given is in fact a solution. So, substitute it in for y and y' and see if the equation holds true.
     
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