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: Solve the nonlinear ODE help

  1. Apr 25, 2009 #1
    1. The problem statement, all variables and given/known data

    Solve the nonlinear ODE

    du/dx=(u+x√(x^2+u^2 ))/(x-u√(x^2+u^2 ))

    by changing variables to x=rcos(theta), u=rsin(theta) and converting the equation to one for d(theta)/dr.

    3. The attempt at a solution

    Not sure if i'm going in the right direction.

    du/dx = du/d(theta) x d(theta)/dx

    u = rsin(theta), du/d(theta) = rcos(theta)
    x = rcos(theta), dx/d(theta) = -rsin(theta),
    i.e. d(theta)/dx = -1/rsin(theta)

    so du/dx = rcos(theta)/-1rsin(theta) = - cos(theta)/sin(theta)

    then i sub x=rcos(theta), u=rsin(theta) in the main equation

    - cos(theta)/sin(theta) = rsin(theta)+rcos(theta)√(r^2sin^2(theta) etc etc..

    so i gather the r^2, and make the sin^2+cos^2 both to one, then the √r^2 goes to just 'r'.

    then i take divide the whole equation by r

    du/dx = -cos(theta)/sin(theta) = [sin(theta)+rcos(theta)]/[rcos(theta)-rsin(theta)

    so i times the sin(theta) over the right side and the other to the right..
    and i get 1=0...

    can someone put me in the right direction on what i did wrong?

    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Apr 25, 2009 #2
    actually the answer is d(theta)/dr = 1, if any of you were wondering.

    needed to differentiate x and u in terms of r and theta with the product rule.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook