Question: How to solve the following ODEs?

Dear experts;

How can I solve this problem with maple?

restart:

 X[3](0):=6.3096*10^9;
 c:=0.67;
 d:=3.7877*10^(-8);
 delta:=3.259*d;
 lambda:=(2/3)*10^8*d;
 R[0]:=1.33;
 p:=(c*X[3](0)*delta*R[0])/(lambda*(R[0]-1));
beta:=(d*delta*c*R[0])/(lambda*p);

ode:=diff(x[1](t), t)=(lambda-d*x[1](t)-(1-beta*x[1](t)*x[3](t)*(psi[1](t)-psi[2](t))/A[1])*beta*x[1](t)*x[3](t)),
 diff(x[2](t), t) =((1-beta*x[1](t)*x[3](t)*(psi[1](t)-psi[2](t))/A[1])*beta*x[1](t)*x[3](t)-delta*x[2](t)),
 diff(x[3](t), t) =((1+psi[3](t)*p*x[2](t)/A[2])*p*x[2](t)-c*x[3](t)),diff(psi[1](t), t) =-1+1/A[1]*beta^2*x[1](t)*(x[3](t))^2*(psi[1](t)-psi[2](t))^2-psi[1](t)*(-d+beta^2*(x[3](t))^2*(psi[1](t)-psi[2](t))/A[1]*x[1](t)-(1-beta*x[1](t)*x[3](t)*(psi[1](t)-psi[2](t))/A[1])*beta*x[3](t))-psi[2](t)*(-beta^2*(x[3](t))^2*(psi[1](t)-psi[2](t))/A[1]*x[1](t)+(1-beta*x[1](t)*x[3](t)*(psi[1](t)-psi[2](t))/A[1])*beta*x[3](t)),
 diff(psi[2](t), t) =1/A[2]*psi[3](t)^2*p^2*x[2](t)+psi[2](t)*delta-psi[3](t)*(psi[3](t)*p^2/A[2]*x[2](t)+(1+psi[3](t)*p*x[2](t)/A[2])*p),
 diff(psi[3](t), t) = 1/A[1]*beta^2*(x[1](t))^2*x[3](t)*(psi[1](t)-psi[2](t))^2-psi[1](t)*(beta^2*(x[1](t))^2*(psi[1](t)-psi[2](t))/A[1]*x[3](t)-(1-beta*x[1](t)*x[3](t)*(psi[1](t)-psi[2](t))/A[1])*beta*x[1](t))-psi[2](t)*(-beta^2*(x[1](t))^2*(psi[1](t)-psi[2](t))/A[1]*x[3](t)+(1-beta*x[1](t)*x[3](t)*(psi[1](t)-psi[2](t))/A[1])*beta*x[1](t))+psi[3](t)*c;

ics := x[1](0)=5.5556*10^7, x[2](0)=1.1111*10^7,x[3](0)=6.3096*10^9,psi[1](100)=0,psi[2](100)=0,psi[3](100)=0;

dsolve([ode, ics],numeric);?????????????????????????

Please help me

ode.mws