1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    User Avatar
    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!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook