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System of non-linear ODE

  1. May 30, 2014 #1
    Hello everybody. Solving a problem in Physics I run into a system of equations that I do not know how to solve, I would appreciate some help. Here is the system:


    \ddot{x}+4\dot{x}^2=C_1e^{y}

    \dot{y}^2=C_2\ddot{x}


    The dependent variables are x,y. C_1 and C_2 are some constants. I try to play with the equations to obtain one equation in one unknown but I dont get anywhere...

    If someone could tell me where I can learn to write the equations so that they appear in math style that would be awesome as well.

    Thank you in advance!!
     
  2. jcsd
  3. May 30, 2014 #2
    Are you sure you've done everything correctly so far and you're indeed meant to solve this analytically? I put the system in Maple, and the solution is quite ugly. I don't know what "Physics I" consists of, but it sounds like something where you wouldn't need to solve something like this.

    You can use [ tex] and [ itex] tags (without the spaces, itex for inline text) to write in LaTeX.
     
  4. May 30, 2014 #3
    Hi Deldeal thanks for your reply.

    I am almost sure the system is setup correctly. I do not need an exact solution but an approximate one i.e. the first few terms in a power series method.

    Best
     
  5. May 30, 2014 #4
    [itex] \ddot{x}+4\dot{x}^2=C_1e^{y} [/itex]

    [itex] \dot{y}^2=C_2\ddot{x} [/itex]


    What happens if you assume that [itex] |y| \ll 1 [/itex] ?

    In this limit what is the Taylor expansion of [itex]e^{y} [/itex] ?
     
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