1. Not finding help here? Sign up for a free 30min 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!

Proving a differential equation using the substitution method

  1. Oct 2, 2008 #1
    1. The problem statement, all variables and given/known data

    dy/dx = [tex]\frac{[2cos(x)^2-sin(x)^2+y^2]}{[2cos(x)]}[/tex]

    Substitute y(x) = sin(x) + [tex]\frac{1}{u(x)}[/tex]
    2. Relevant equations

    By doing the substitution, it will yield the differential equation for u(x)

    du/dx = -u tan(x) - [tex]\frac{1}{2}[/tex]sec(x)

    3. The attempt at a solution

    I figured out i have to use chain rule. However, if du/dx = du/dy x dy/dx , which dy/dx do i choose? It can be either

    this - dy/dx = [tex]\frac{[2cos(x)^2-sin(x)^2+y^2]}{[2cos(x)]}[/tex]

    or - y = sin(x) + 1/[u(x)]
    dy/dx = cos(x)

    Then, I found the dy/du from this equation y = sin(x) + 1/[u(x)] and flipped it around to get du/dy. After multiplying using the chain rule, I dont get the differential equation as shown. Please help me out here. =X
     
  2. jcsd
  3. Oct 2, 2008 #2
    I just realized a similar question has been posted. Please close the thread. Sorry for the trouble. =X
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?