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Solve the given clairaut equation

  1. Feb 11, 2016 #1
    1. The problem statement, all variables and given/known data
    Screen Shot 2016-02-11 at 1.16.04 PM.png

    2. Relevant equations
    x=-f'(t)
    y=f(t)-tf'(t)

    3. The attempt at a solution
    Solution in picture. This is the solution to this problem, but I have no idea where the y^2=4t^6 comes from. Doin this problem I get everything up until y=2t^3 and then using x=3t^2 I solved for t and plugged it in, but that's not working. I did every other clairaut's problem like this, but I have no idea where this one goes after the y=2t^3 step.
     
  2. jcsd
  3. Feb 11, 2016 #2

    LCKurtz

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    You have ##x = 3t^2## and ##y=2t^3##. He is just eliminating the ##t## by noting if you cube the ##x## and sqare the ##y## both equations will have a ##t^6## so you can eliminate it easily.

    It would be much easier to follow the thread if you would type the equations instead of posting images, as per forum rules.
     
  4. Feb 11, 2016 #3
    ohhhhhhh. I see that now. Thank you!!!! :smile:
     
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