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Homework Help: 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
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