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: Non Linear ODE

  1. Sep 29, 2010 #1
    1. The problem statement, all variables and given/known data

    [tex]\left(\frac{dy}{dx}\right)^2 - 4x\frac{dy}{dx} + 6y = 0[/tex]

    2. Relevant equations

    A common approach we have used for similar problems has been to let P = dy/dx


    3. The attempt at a solution

    Doing so we have:

    [tex]P^2 - 4xP +6y = 0[/tex]

    [tex]\Rightarrow 6y = 4P(x - P)[/tex]

    Differentiating gives:

    [tex]6P = 4\left[P(1 - \frac{dP}{dx}) +\frac{dP}{dx}(x - P)\right] = 0[/tex]


    Now usually we try to factor this and solve each factor as a linear 1st order EQ in P. However, I am having trouble seeing a nice way to factor this, that makes each factor linear. All I can get to is

    [tex]-2\left[P+2\frac{dP}{dx} - 2x\frac{dP}{dx} + 2P\frac{dP}{dx}\right] = 0[/tex]


    Any thoughts on what to do with the bracketed term to get 2 linear EQs out of the deal?

    Thanks :smile:
     
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

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