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DIFFERENTIAL EQUATION SYSTEM

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momo
2011-08-28
2012-11-20
  • momo
    momo
    2011-08-28

    Hello
    There is a function(or packages) in REDUCE the a differential equation system is converted to a linear DES?
    In other words a function to solve a non-linear or homogene differential equation(no odesolve)
    for example how to solve the differential equation system
    DF(x,u) = y + sin(u)
    DF(y,_u) = z
    DF(z,_u) =-y+cos(u)

    Thank you

     
  • Francis Wright
    Francis Wright
    2011-08-30

    Take a look at the CRACK package, which is distributed with REDUCE.

    Francis

     
  • thomasjwolf
    thomasjwolf
    2011-08-30

    Should _u in the 2. and 3. equation be u?
    If x=x(u), y=y(u), z=z(u) then the system is already linear in x,y,z. This actually is a system of 2 equations (2. and 3.) for 2 functions y,z and if they are solved the x is computed from the first equation. To solve the 2. and 3. equation I would
    substitute z from the 2. into the 3. giving a 2nd order ODE with sin(u), cos(u) solutions of the homogeneous part and then make coefficients u-dependent,, substitute and compute them to solve the inhomogeneous 2nd order ODE.

    Thomas

     
  • momo
    momo
    2011-08-31

    Hello,
    Thanks for your help.
    I'm going to look like it works with crack.
    Thank you