Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Solve these differential equations by converting to Clairaut's form

  1. Jul 4, 2013 #1
    The question comprises of three subparts which need to be converted to Clairaut's form and then solved :

    (a) x p2 - 2yp + x + 2y = 0

    (b) x2 p2 + yp (2x + y) + y2 = 0

    (c) (x2+y2)(1+p)2-2(x+y)(1+p)(x+yp)+(x+yp)2=0

    Note : p = dy/dx

    I understand that Reducing to Clairaut's form involves suitable substitution so as to bring it in the form of V = P U + f(P) but i am unable to form any intuition about what such substitutions might be , as the above equations seem complicated with more than one combination of variables and 'p'.

    I have added three sub-parts to get a better understanding of the intuition involved in such substitutions. Help would be greatly appreciated. Thanks.
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted



Similar Discussions: Solve these differential equations by converting to Clairaut's form
Loading...