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

First Order Nonlinear PDE

  1. Jan 7, 2010 #1
    i have to solve this equation :

    du/dx * du/dy = x*y

    u(x,y) = x for y =0

    with putting this equation in the form : F(x,y,u,du/dx,du/dy) = 0 . it can be solved.
    But mine book does not explain how to do this, there are no examples.

    Can someone help me ? or any links of examples on the internet?
     
  2. jcsd
  3. Jan 7, 2010 #2
    Your PDE already is in a such form!?

    If you suppose that

    u(x,y)=A(x)*B(y)

    then substitution such u into PDE gives you after separation of variables

    diff(A(x),x)*A(x)/x=1/(B(y)*diff(B(y),y)/y)=c ,

    where c is a constant. Solutions of these two ODEs lead to particular solution

    u(x,y) = (c*x^2+C2)^(1/2)*1/c*(c*(y^2+C1*c))^(1/2)

    (among other things this solution allows to obtain the general sulution to your PDE!).
    If now substitute y=0 into above solution, we find that it must be

    C2=0, C1=1/c

    so the required solution is as follows

    u(x,y) = x*(y^2+1)^(1/2)
     
  4. Jan 8, 2010 #3
    Thank you for giving the answer. Mine mistake I had to tell, to solve this problem we had to use method of characteristics. I did it and found the same answer. so it is correct.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: First Order Nonlinear PDE
  1. Nonlinear first order (Replies: 4)

  2. Nonlinear first order DE (Replies: 22)

  3. First order nonlinear (Replies: 1)

  4. First order PDE help (Replies: 2)

Loading...