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Homework Help: Differential Question

  1. Jun 30, 2010 #1
    1. The problem statement, all variables and given/known data

    Hi Guys,
    I've got a couple of examples of de's in my lecture notes. one is:
    [itex]y'=1+x^2[/itex]
    which has a general solution of [itex]y= x+\frac{x^3}{3} + c[/itex]
    which i I understand they have taken the integral wrt [itex]x[/itex]


    the second is

    [itex]y'=1+y^2[/itex] which has a general solution of [itex]y= [/itex]tan[itex](x+c)[/itex]

    Can some one please explain to me how that got the second solution?
     
  2. jcsd
  3. Jun 30, 2010 #2

    Mark44

    Staff: Mentor

    Both problems can be done by the technique of separation of variables.

    For the first, you have
    dy/dx = 1 + x^2
    ==> dy = (1 + x^2)dx
    Integrate both sides to get what you already have shown.

    For the second, you have
    dy/dx = 1 + y^2
    ==> dy/(1 + y^2) = dx
    Now integrate both sides to get
    arctan(y) = x + C ==> y = tan(x + C).
     
  4. Jun 30, 2010 #3
    Thanks mate I had forgoten about separation of variables.
    I was integrating both sides wrt x in the second example.
     
  5. Jun 30, 2010 #4

    Mark44

    Staff: Mentor

    And good luck with that!:biggrin:
     
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