Results 1 to 5 of 5

Math Help - is my solution correct?

  1. #1
    Newbie
    Joined
    Jan 2010
    Posts
    6

    Smile is my solution correct?

    Hi, i attempted this question, but not sure whether it is correct or not..

    using separation of variables:

    X''(x)=S X(x) , Y''(y)=-S Y(y), where S is separation constant

    becos X'(0)=0, X'(1)=0, so using the boundary value table i get:

    S=(npi)^2

    X=cos(n pi x) n=0,1,2....

    Y=Acos*square root of S * y + Bsin* square root of S * y

    since Y(0)=0

    so Y=Bsin(n pi y)

    so X(x)Y(y)=Bcos(n pi x)* sin(n pi y)



    i know it's not finished, but is it correct from here? cos i dont feel quite sure about it....thank you~
    Attached Thumbnails Attached Thumbnails is my solution correct?-q.jpg  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,419
    Thanks
    1855
    Quote Originally Posted by lollol View Post
    Hi, i attempted this question, but not sure whether it is correct or not..

    using separation of variables:

    X''(x)=S X(x) , Y''(y)=-S Y(y), where S is separation constant

    becos X'(0)=0, X'(1)=0, so using the boundary value table i get:

    S=(npi)^2
    No, that's impossible. If X is a trig function (and it must be for its derivative to be 0 at 0 and 1), then S must be negative: you must mean S= -(n\pi)^2.

    X=cos(n pi x) n=0,1,2....


    Y=Acos*square root of S * y + Bsin* square root of S * y
    and now, because S is negative, -S is positive. Y"= n\pi Y so Y is exponential or hyperbolic: I would use Y(y)= C cosh(y)+ D sinh(y) because then Y(0)= C cosh(0)+ D sinh(0)+ C(1)+ D(0)= C= 0.

    since Y(0)=0

    so Y=Bsin(n pi y)

    so X(x)Y(y)=Bcos(n pi x)* sin(n pi y)



    i know it's not finished, but is it correct from here? cos i dont feel quite sure about it....thank you~
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jan 2010
    Posts
    6
    thanks hallsofivy, from ur solution, i would get Y=Dsinh(n pi y), and for X, since

    . so it involves complex number after substituting S into the equation,
    therefore X=Acos(n pi x) + Bsin(n pi x)

    does it seem right?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,419
    Thanks
    1855
    Yes, you had X correct all along: X(x)= A cos(n pi x).

    Your entire solution will be a sum such as \sum_n C cos(n\pi x)Sinh(\pi y).
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Jan 2010
    Posts
    6

    hi

    sry.. but i think i am stuck again..while i continue with my work, i got An=0.. i dont quite understand why i got that, so i think may be i am wrong? please see the attachment, thank you
    Attached Thumbnails Attached Thumbnails is my solution correct?-1.gif  
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: March 10th 2011, 09:12 AM
  2. Extremal - Is my solution correct?
    Posted in the Calculus Forum
    Replies: 6
    Last Post: September 11th 2010, 08:50 PM
  3. Is my solution correct?
    Posted in the Differential Equations Forum
    Replies: 8
    Last Post: April 19th 2010, 01:41 AM
  4. Is it correct solution?
    Posted in the Calculus Forum
    Replies: 2
    Last Post: January 28th 2010, 08:26 PM
  5. is my solution correct ..
    Posted in the Advanced Applied Math Forum
    Replies: 12
    Last Post: August 24th 2009, 11:01 PM

Search Tags


/mathhelpforum @mathhelpforum