Question: CLOSED FORM SOLUTION OF ISOSPECTRAL FLOW EQUATIONS

To anyone out there who may be able to help

I have been researching into closed-form solutions of the 2 x 2 case of the Matrix Differential Equations

dM(s)/ds = [ M(s) , D(s)/2 ]   ,    M(0) = Mo in sl(2,R)  ( 1 )

dD(s)/ds = [ M(s) , K(s) ]      ,     D(0) = Do in sl(2,R)  ( 2 )

dK(s)/ds = [ D(s)/2 , K(s) ]    ,    K(0) =  Ko in sl(2,R)  ( 3 )

where s is a real-valued parameter.

Now if

M(s) := [ [ m[1](s) , m[2](s) ] , [ m[3](s) , -m[1](s) ] ]  ( 4 )

D(s) := [ [ d[1](s) , d[2](s) ] , [ d[3](s) , -d[1](s) ] ]        ( 5 )

K(s) := [ [ k[1](s) , k[2](s) ] , [ k[3](s) , -k[1](s) ] ]        ( 6 )

it is readily shown that

dm[1](s)/ds = ( m[2](s).d[3](s) - m[3](s)*d[2](s) )/2  ,  m[1](0) = m1o  ( 7 )

dm[2](s)/ds = m[1](s).d[2](s) - m[2](s).d[1](s)           ,  m[2](0) = m2o  ( 8 )

dm[3](s)/ds = m[3](s).d[1](s) - m[1](s).d[3](s)            , m[3](0) = m3o ( 9 )

dd[1](s)/ds =  m[2](s).k[3](s) - m[3](s)*k[2](s)            , d[1](0) = d1o ( 10 )

2.m[1](s).k[1](s) + m[2](s).k[3](s) + m[3](s).k[2](s) + d[1](s)^2 + d[2](s).d[3](s) 

= 

2.m1o.k1o + m2o.k3o + m3o.k2o + d1o^2 + d2o.d3o  ( 18 ) 

2.d[1](s).k[1](s) + d[2](s).k[3](s) + d[3](s).k[2](s)  = 2.d1o.k1o + d2o.k3o + d3o.k2o  ( 19 ) 

k[1](s)^2 + k[2](s).k[3](s) == k1o^2 + k2o.k3o  ( 20)

My first question is are there any other linearly independent first integrals and can Maple ( I have Maple 13 ) be used to find them ? ? ?

Both Maple 13 and Mathematica 7 fail to solve the nine coupled quadratic homogeneous ordinary differential equations.

Please help me if you can.   Peter Van Eetvelt.

using dsolve ( Maple ) and DSolve ( Mathematica ) , but I suspect a dedicated Maple program  based on Lie Symmetries may do better.