Results 1 to 2 of 2
Like Tree1Thanks
  • 1 Post By MarkFL

Math Help - Please help for finding 2 Linearly Independent solutions of ....

  1. #1
    Junior Member
    Joined
    Sep 2012
    From
    NY
    Posts
    32

    Please help for finding 2 Linearly Independent solutions of ....

    Please help for finding 2 Linearly Independent solutions of

    x2y'' + xy' + 4y = 0

    my method:

    factoring first
    let y=xA so y' = Ax(A-1) and y'' = A(A-1)x(A-2)

    So A(A-1) + A + 4 =0
    which is A2 + 4 = 0
    A = +/- 2i

    then I don't know how to find 2 LI solutions, please help..
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: Please help for finding 2 Linearly Independent solutions of ....

    One way to proceed would be to use Euler's formula:

    y_1=c_1x^{2i}=c_1e^{\ln(x^{2i})}=c_1e^{2\ln(x)i}=c  _1(\cos(2\ln(x))+i\sin(2\ln(x)))

    y_2=c_2x^{-2i}=c_2e^{\ln(x^{-2i})}=c_2e^{-2\ln(x)i}=c_2(\cos(2\ln(x))-i\sin(2\ln(x)))

    By the principle of superposition, we then find:

    y_1=c_1\cos(2\ln(x))

    y_2=c_2\sin(2\ln(x))
    Thanks from angelme
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Maximum number of linearly independent solutions
    Posted in the Differential Equations Forum
    Replies: 4
    Last Post: January 3rd 2012, 08:33 AM
  2. linearly dependent in Q, linearly independent in R
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: April 12th 2011, 01:44 PM
  3. Replies: 8
    Last Post: July 9th 2008, 12:09 PM
  4. Linearly independent real solutions
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: May 19th 2008, 10:44 AM
  5. Linearly Independent
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: March 25th 2007, 07:55 PM

Search Tags


/mathhelpforum @mathhelpforum