Results 1 to 10 of 10

Math Help - Difficult non-linear system of two differential equations

  1. #1
    Junior Member
    Joined
    May 2010
    Posts
    69

    Difficult non-linear system of two differential equations

    Hello people! Here is the problem. Some ideas for analytical solutions of system of equations? Ai constants.

    A1*x1''*x2*Cos(x1) - A2*x''*Sin(x1)- A3*x1'' + A4*((x2')^2)*Cos(x1) + A5*Sin(x1)=0

    -A6*x1''+A7*x1''*x2*Cos(x1)-A8*x1''*Sin(x1)-A9*((x1')^2)x2*Sin(x1)-A10*((x1')^2)*Cos(x1)+A11=0

    We know x1(0), x2(0), x1'(0), x2'(0).

    Thank you in advance!

    Kind regards!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Jester's Avatar
    Joined
    Dec 2008
    From
    Conway AR
    Posts
    2,361
    Thanks
    39
    Are all the constants a_i, i = 1 \, \cdots \, 11 nonzero and truely arbitrary?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    May 2010
    Posts
    69
    Yes
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Jester's Avatar
    Joined
    Dec 2008
    From
    Conway AR
    Posts
    2,361
    Thanks
    39
    Are you interested in analytical solutions in which some of the constants are zero or related to one another?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    May 2010
    Posts
    69
    Constants are constants like in all of differential equations. All of them are non-zero. I need some of ideas for solving using some analytical method.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Junior Member
    Joined
    May 2010
    Posts
    69
    In first equation it should be A2*x2''*Sin(x1). Constants are linearly independent.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Junior Member
    Joined
    May 2010
    Posts
    69
    Dear Danny,

    This is a fullsimplify form of equations where I replace the constants with Ai. All of them must be in equations. Thank you a lot for take this into consideration.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Junior Member
    Joined
    May 2010
    Posts
    69
    Maybe I can find numerical solutions, but only for determined constants. In this case I can't see how constants affect on solutions. Because of that I need analytical method for solving. But how???
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Junior Member
    Joined
    May 2010
    Posts
    69
    What do you think about perturbation method after approximation of Sin and Cos with polynomial form?
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Junior Member
    Joined
    May 2010
    Posts
    69
    I have forgotten to say that constants Ai are known. I will find how x1[t] and x2[t] depend of [t, A1,A2,A3...] like solution. Is it so hard?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. System of Linear Differential Equations with Constant Coefficients
    Posted in the Differential Equations Forum
    Replies: 8
    Last Post: February 28th 2011, 04:51 AM
  2. Replies: 4
    Last Post: April 23rd 2010, 07:11 AM
  3. Replies: 2
    Last Post: August 27th 2009, 03:52 AM
  4. Difficult Differential Equation System
    Posted in the Differential Equations Forum
    Replies: 0
    Last Post: August 8th 2009, 05:17 PM
  5. system of equations - (difficult problem)
    Posted in the Algebra Forum
    Replies: 4
    Last Post: May 4th 2008, 11:53 PM

Search Tags


/mathhelpforum @mathhelpforum