Results 1 to 6 of 6

Math Help - HELP!! differential equation and bessels function

  1. #1
    Junior Member
    Joined
    Jun 2008
    Posts
    28

    HELP!! differential equation and bessels function

    Hi,
    I'm studying for my final exam at the moment and i found this question from the past exam paper. but i have no idea how to solve it.
    can anyone please please help me!!!

    thanks!!!!!!
    Attached Thumbnails Attached Thumbnails HELP!! differential equation and bessels function-.jpg  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by panda View Post
    Hi,
    I'm studying for my final exam at the moment and i found this question from the past exam paper. but i have no idea how to solve it.
    can anyone please please help me!!!

    thanks!!!!!!
    Make the change of variable y'=y/x^{\alpha} and rewrite the de in terms of y' and x. Then put x'=\beta x^{\gamma} and you should find that x' and y' satisfy the Bessel equation of order n.

    RonL
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Jun 2008
    Posts
    28
    thanks for the reply
    just one more question.
    how do you know which variable to use??
    for instance, how do you choose the 'change of variable'?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by panda View Post
    thanks for the reply
    just one more question.
    how do you know which variable to use??
    for instance, how do you choose the 'change of variable'?
    By comparing the Bessel equation with that given, and more directly looking at the form of the solution that you are to demonstrate. (in fact the suggested change of variables comes directly from the suggested solution)

    RonL
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Jun 2008
    Posts
    28
    using
    i got
    (y'x^2 - yxalpha)x^-alpha + yxx^-alpha - (2alphaxy)x^-alpha + beta^2.gemma^2.x^2gamma + alpha^2 -n^2.gemma^2)y = 0

    is this right???? and i wasnt sure how to use x'=beta.x^gemma from here.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by panda View Post
    using
    i got
    (y'x^2 - yxalpha)x^-alpha + yxx^-alpha - (2alphaxy)x^-alpha + beta^2.gemma^2.x^2gamma + alpha^2 -n^2.gemma^2)y = 0

    is this right???? and i wasnt sure how to use x'=beta.x^gemma from here.
    You do know that the ' do not denote differentiation here don't you?

    Try instead u(x)=y(x)/x^{\alpha} first, from this compute \frac{dy}{dx} and \frac{d^2y}{dx^2} in terms of x, u, \frac{du}{dx} and \frac{d^2u}{dx^2} and substitute into the DE.

    RonL
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. differential equation containing bessel function in RHS
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: April 21st 2011, 04:36 AM
  2. Differential Equation to Transfer Function
    Posted in the Differential Equations Forum
    Replies: 5
    Last Post: May 13th 2010, 01:13 PM
  3. Proving eigenfunctions of Bessels equation are orthogonal
    Posted in the Differential Equations Forum
    Replies: 0
    Last Post: September 22nd 2009, 04:21 PM
  4. Transfer function by differential equation
    Posted in the Differential Equations Forum
    Replies: 4
    Last Post: September 4th 2009, 03:28 AM
  5. Help me ! A function satisfies the differential equation
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: February 11th 2009, 10:28 AM

Search Tags


/mathhelpforum @mathhelpforum