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Solve this differential equation using separation of variables

  1. Apr 7, 2012 #1
    Solve the following first order, ordinary differential equations using separation of variables:

    dy/dx = y^2 x

    subject to y=-1 when x=0

    the correct answer is: y = -2/x^2 + 2

    i cannot seem to get this answer, after i separate the variables and integrate both sides i get:

    y^2 x^2/2

    then if i plug the values in i get y = 0????

    please help
     
  2. jcsd
  3. Apr 7, 2012 #2

    rock.freak667

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    When you separate the variables you should get

    (1/y^2)dy = x dx

    Integrating 1/y^2 wrt y will not give you y^2. Rewrite it as y^-2.
     
  4. Apr 7, 2012 #3
    hi, thanks foryour reply i appreciate it, but could you please explain why when you separate variables y^2 become 1/y^2?
     
  5. Apr 7, 2012 #4

    rock.freak667

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    dy/dx = y2 x

    Divide both sides by y2

    (1/y2)dy/dx = x
     
  6. Apr 7, 2012 #5
    where has the 1 come from? is it the coefficiant of dy/dx?
     
  7. Apr 7, 2012 #6

    rock.freak667

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    Well you can think of the 1 like that yes.
     
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