Results 1 to 3 of 3

Math Help - Decomposition of 2 fourth order differential equations on 4 equations of second order

  1. #1
    Junior Member
    Joined
    May 2010
    Posts
    69

    Decomposition of 2 fourth order differential equations on 4 equations of second order

    How to make decomposition of 2 fourth order differential equations on 4 equations of second order, just that!

    C1x''''+C2x'''+C3x''+C4x'+C5x-C6y''-C7y=0

    D1y''''+D2y'''+D3y''+D4y'+D5y-D6x''-D7x=0

    Known constants Ci, Di

    Thank you in advance
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    Quote Originally Posted by derdack View Post
    How to make decomposition of 2 fourth order differential equations on 4 equations of second order, just that!

    C1x''''+C2x'''+C3x''+C4x'+C5x-C6y''-C7y=0

    D1y''''+D2y'''+D3y''+D4y'+D5y-D6x''-D7x=0

    Known constants Ci, Di

    Thank you in advance
    Use the substitutions

    v=x'' \quad w=y''

    This gives

    C_1v''+C_2v'+C_3v+C_4x'+C_5x-C_6w-C_7y=0

    D_1w''+D_2w'+D_3w+D_4y'+D_5y-D_6v-D_7x=0

     x''=v

    y''=w
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    May 2010
    Posts
    69
    Substitution is ok, but I need 4 equations of second order because I must got the system which is the same with some which I already have. To see which influence have the different constants on some parts of equations. I must got system like this one:

    q1''+A1*q1'+A2*q1-A3*q2=0
    q2''+B1*q2'+B2*q2-B3*q1=0

    I know that my system can not reduce on this one, but I can maybe ignore some of high derivative of functions?

    What will be the difference between this two equations generally.

    q1''''+a*q1''+b*q1-c*q2=0 and then we ignore q1'''', yields q1''+b1*q1-c1*q2=0, then if I already have this equation q1''+b3*q1-c3*q2=0, I know that the difference first is number of solutions, but I must compare the solutions which is associated with the same case of equations???
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: July 20th 2011, 04:04 PM
  2. Replies: 5
    Last Post: March 15th 2010, 01:44 PM
  3. Replies: 2
    Last Post: February 23rd 2009, 06:54 AM
  4. Replies: 5
    Last Post: July 16th 2007, 05:55 AM
  5. Replies: 3
    Last Post: July 9th 2007, 06:30 PM

Search Tags


/mathhelpforum @mathhelpforum