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: Solving second order linear homogeneous differential equation

  1. May 9, 2012 #1
    1. The problem statement, all variables and given/known data

    Find the set of functions from [itex](-1,1)→ℝ[/itex] which are solutions of:

    [itex](x^{2}-1)\frac{d^{2}y}{dx^{2}}+x\frac{dy}{dx}-4y = 0[/itex]

    2. Relevant equations

    3. The attempt at a solution

    There is a hint which says to use the change of variable:

    doing this I get:

    [itex]\frac{dx}{dθ} = -sin(θ)[/itex]


    [itex]dx = -sin(θ)dθ[/itex]


    [itex](a): \frac{dy}{dx} = \frac{dy}{dθ}\frac{1}{-sin(θ)}[/itex]

    [itex](b): \frac{d^{2}y}{dx^{2}} = \frac{d^{2}y}{dθ^{2}}\frac{1}{sin^{2}(θ)}[/itex]

    Can I do this?!?

    If so, substituting everything in gives:

    [itex]-sin^{2}(θ)\frac{d^{2}y}{dθ^{2}}\frac{1}{sin^{2}(θ)} + cos(θ)\frac{dy}{dθ}\frac{1}{-sin(θ)} - 4y = 0[/itex]


    [itex]y'' + cot(θ)y' + 4y = 0[/itex]

    Now.... I am not sure.
    Have I made some mistake?
    Or should I be able to solve this?
    Could someone please point me in the right direction?
    Thanks a lot!
  2. jcsd
  3. May 9, 2012 #2


    User Avatar
    Science Advisor
    Homework Helper

    hi the0! :smile:
    no, your (b) doesn't include dy/dθ d/dx(-1/sinθ)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook