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End of differential equation, quick alegbra Q

  1. Jan 30, 2012 #1
    1. The problem statement, all variables and given/known data
    I just solved a differential equation and got the problem down to its implicit solution:
    y/√(1+y2) = x3+C where C is an arbitrary constant
    My question now is, how can I solve for y? I can't get past the algebra. Thanks!


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jan 30, 2012 #2

    Dick

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    Science Advisor
    Homework Helper

    Square both sides. Solve for y^2. Take a square root. Come on. Try it.
     
  4. Jan 30, 2012 #3
    Square both sides and bring the bottom part to the other side. You'll get

    [itex]y^2 = (1+y^2)(x^3 + c)^2[/itex]

    Then multiply out and regroup.

    [itex]y^2 -y^2(x^3 + c)^2 = (x^3 + c)^2[/itex]

    then you'll get [itex] y^2 = \frac{(x^3+c)^2}{1-(x^3+c)^2}[/itex]

    So [itex]y = \sqrt{\frac{(x^3+c)^2}{1-(x^3+c)^2}}[/itex]
     
  5. Jan 30, 2012 #4
    thank you!
     
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