how to solve this differential equation



Dear all,

I got problem to solve this differential equation, hope some one can help me
on this
here my code problem and maxima code

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eq1:diff(f(s),s)=-sqrt(3)*g(s)*k$
eq2:diff(g(s),s)=k*(sqrt(3)*f(s)-2^(3/2)*h(s))$
eq3:diff(h(s),s)=k*(2^(2/3)*g(s)-3*l(s))$
eq4:diff(l(s),s)=3*k*h(s)$

atvalue(f(s),s=0,f610)$
atvalue(g(s),s=0,0)$
atvalue(h(s),s=0,1/2*sqrt(3)*k*f610/sqrt(2))$
atvalue(l(s),s=0,0)$

desolve([eq1,eq2,eq3,eq4],[f(s),g(s),h(s),l(s)]);

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but then I get result with ilt solution and I assume that maxima failed to
give me the correct answer,

so I try to use ode2 command,

I sort the eq1 and eq3 manually(can we do using maxima?), and I get below
equation

eqn1:'diff(f,s,2)+3*x^2*f=2*sqrt(2)*sqrt(3)*g;
eqn3:'diff(g,s,2)+17*x^2*g=2*sqrt(2)*sqrt(3)*f;

so I give ode2 command for both equation, x is nonzero,

eqn2:ode2(eqn1,f,s);
eqn4:ode2(eqn3,g,s);

maxima give me some pretty result I think, but how to combine both equation
and give ic1 or ic2 command to both result because both of them dependent on
each other.

can someone help me on this

i try to get all solution for f(s),g(s),h(s) and l(s),

thanks a lot