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Trouble separating equation (differential equation)

  1. Apr 12, 2010 #1
    1. The problem statement, all variables and given/known data
    y' = (2x) / y+(x^2)y y(0) = -2
    i realize this is sort of algebra prob, but i cant seem to separate x's from y's..



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Apr 12, 2010 #2

    Mark44

    Staff: Mentor

    [tex]y' = \frac{2x}{y(1 + x^2)}[/tex]

    Now try separating it.
     
  4. Apr 12, 2010 #3
    wow. that shouldve been obvious.
    thanks.
     
  5. Apr 12, 2010 #4
    Please check my work thanks alot..
    find solution in explicit form:

    y' = (2x) / y+(x^2)y initial conditions: y(0) = -2

    dy/dx = 2x/y(1+x^2)

    y dy = 2x + (2/x) dx

    integrate both sides...

    (1/2)y^2 = x^2 + 2ln|x| + c

    y^2 = 2x^2 + 4ln|x| + 2c

    y = root [2x^2 + 4ln|x| + c]

    apply IC:

    -2 = root [2(0)^2 + 4ln|0| + c]

    -2 = (root 4) + c

    c = -4 (i am reasong that root c is same as c because whether its root c or just c, both are still constants.. right?)

    so my solution is:
    y = root [2x^2 + 4ln|x| -4]
     
  6. Apr 12, 2010 #5

    Mark44

    Staff: Mentor

    Mistake in line above. It looks like you are trying to say that 2x/(1 + x^2) = 2x/1 + 2x/x^2.

    That's just like saying that 2/(4 + 8) = 2/4 + 2/8 = 1/2 + 1/4 = 3/4, which I hope you can see is not true.

    If you are working with differential equations, you shouldn't be having problems with basic algebra manipulation.
     
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