Question: how to solve for x1(t), x2(t), x3(t)

i copy from notepad, it do not have line return, so i copy to MS WORD and copy here from MS WORD

but some characters missing, if there is some missing please tell me, it seems old web page is better

code and error here

https://skydrive.live.com/redir?resid=E0ED7271C68BE47C!351

restart;with(LinearAlgebra):

f:=[x3-x2^3,-x2,x1^2-x3]:

g:=[0,-1,1]:

fv:=:

gv:=<0,-1,1>:

u := -Physics[`*`](Physics[`*`](Physics[`*`](3, Physics[`^`](x2(t), 2)), x2(t))+Physics[`^`](x1(t), 2)-x3(t), Physics[`^`](1+Physics[`*`](3, Physics[`^`](x2(t), 2)), -1));

- diff( ,t)

ff := ;

u := -Physics[`*`](Physics[`*`](Physics[`*`](3, Physics[`^`](x2(t), 2)), x2(t))+Physics[`^`](x1(t), 2)-x3(t), Physics[`^`](1+Physics[`*`](3, Physics[`^`](x2(t), 2)), -1)); - diff( ,t)ff := ;

idea 1

sys_ode := diff(u,x1(t))=0,diff(u,x2(t))=0,diff(u,x3(t))=0;

dsolve([sys_ode],[x1(t),x2(t),x3(t)]);

i use Euler, above dsolve can not be solved

Idea 2 diff(x,t) = f + g*u

fv + DotProduct(gv, [u,u,u]);  # since can not use this DotProduct, i manual type it as follow

sys := fv + DotProduct(gv, [u,u,u]);

dsolve(diff(x1(t),t) = sys[1], x1(t));

dsolve(diff(x2(t),t) = sys[2], x2(t));

dsolve(diff(x3(t),t) = sys[3], x3(t));

as i do not know whether dsolve separately or solve in one system as follow, i do twice

above doing separately, x2(t) and x3(t) can not be solved have error, how to do?

sys2 := diff(x1(t),t) = sys[1], diff(x2(t),t) = sys[2], diff(x3(t),t) = sys[3];

dsolve(sys2, {x1(t),x2(t),x3(t)});

 then try to dsolve in one system, it got nothing, where is wrong?

> dsolve(diff(x1(t), t) = sys[1], x1(t)); dsolve(diff(x2(t), t) = sys[2], x2(t)); dsolve(diff(x3(t), t) = sys[3], x3(t));

                           /       3\       

                   x1(t) = \x3 - x2 / t + _C1

Error, (in dsolve) x2(t) and x2 cannot both appear in the given ODE.

Error, (in dsolve) x3(t) and x3 cannot both appear in the given ODE.

> sys2 := diff(x1(t), t) = sys[1], diff(x2(t), t) = sys[2], diff(x3(t), t) = sys[3]; dsolve(sys2, [x1(t), x2(t), x3(t)]);

        d                 3 

       --- x1(t) = x3 - x2 ,

        dt                  

                                  3        2         

          d                3 x2(t)  + x1(t)  - x3(t) 

         --- x2(t) = -x2 + -------------------------,

          dt                                2        

                                 1 + 3 x2(t)         

                                       3        2       

          d            2        3 x2(t)  + x1(t)  - x3(t)

         --- x3(t) = x1  - x3 - -------------------------

          dt                                     2      

                                      1 + 3 x2(t)       

Error, (in dsolve) found wrong extra argument(s): diff(x2(t), t) = -x2+(3*x2(t)^3+x1(t)^2-x3(t))/(1+3*x2(t)^2), diff(x3(t), t) = x1^2-x3-(3*x2(t)^3+x1(t)^2-x3(t))/(1+3*x2(t)^2), [x1(t), x2(t), x3(t)]