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Solve this Cauchy-problem (PDE)

  1. Oct 9, 2015 #1
    1. The problem statement, all variables and given/known data
    Find the general solution of Solve yux - xuy = xyu2

    Next, solve the Cauchy problem with the Cauchy data x = y = u
    2. Relevant equations

    3. The attempt at a solution
    My teacher told us we should investigate how to solve this. The problem is we just have seen linear first order PDE, but this is non-linear! Could you please give me a hint or a name to start with?
    Last edited: Oct 9, 2015
  2. jcsd
  3. Oct 9, 2015 #2


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    Homework Helper

    Assume u is not zero. Apply your condition that x=y=u and divide out a factor of u.
  4. Oct 9, 2015 #3
    I'm terrible sorry I didn't state the problem correctly. First I must find the general solution and next the condition x = y = u.
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