Hi,
Ok, to solve, say, 253th order system of differential equations with
many functions one can simply write:
y=function('y',x)
y1=diff(y,x,1)
y2=diff(y1,x,2)
y3=diff(y2,x,3)
...
y253=diff(y252,x,253)
z=function('z',x)
z1=diff(z,x,1)
z2=diff(z1,x,2)
z3=diff(z2,x,3)
...
z253=diff(z252,x,253)
etc.
and then rewrite original differential equations for these new
functions. It should then become 1st order differential equation
system.
Eqn1 = (expression of above listed functions)_1 == 1
Eqn2 = (expression of above listed functions)_2 == 1
Eqn3 = (expression of above listed functions)_3 == 1
...
Eqn100 = (expression of above listed functions)_100 == 1
...
Eqn_n = (expression of above listed functions)_n == 1
Then desolve_system can be used to solve the functions
y,y1,y2,...,y253,z,z1,z2,...,z253 etc. If n<(number of functions to be
solved), the solution will probably include some independent
constants.
The problem is then, whether original equations can be made 1st order
using this way.
Thank you for your time.
Jari-Pekka Ikonen
On Dec 15, 8:12 pm, "[email protected]" <[email protected]> wrote:
> You may want to try Sage 4.3.rc1 and something like this
>
> sage: y=function('y',x)
> sage: desolve_laplace(diff(y,x,6) == y,y,ivar=x,ics=[0,1,2,5,6,7,3])
> 1/6*(sqrt(3)*sin(1/2*sqrt(3)*x) - 3*cos(1/2*sqrt(3)*x))*e^(-1/2*x) -
> 1/6*(3*sqrt(3)*sin(1/2*sqrt(3)*x) + 17*cos(1/2*sqrt(3)*x))*e^(1/2*x) +
> 1/3*e^(-x) + 4*e^x
>
> Or install patchhttp://trac.sagemath.org/sage_trac/ticket/6479
>
> Robert
>
> On 15 pro, 12:19, "Jari-Pekka Ikonen" <[email protected]>
> wrote:
>
>
>
> > Hello,
>
> > I wrote in Sage:
>
> > maxima.clear('x'); maxima.clear('fnth')
>
> > maxima.de_solve_Laplace("diff(fnth(x),x,60) = fnth(x)", ["x","fnth"], [0,1,5
> > 2,3,65,8,9,5,43,2,4,5,6,5,3,2,4,6,76,8,7,56,4,3,3,4,5,6,8,9,7,5,4,3,4,5,6,7
> > 9,7,5,4,4,3,4,5,6,7,7,6,5,4,3,5,6,6,5,5,4,4])
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