# Question:How to find the solutions matrix(array) of ode

## Question:How to find the solutions matrix(array) of ode

Maple 2021

How to find Z(t) matrix(array) =[ [z[1,0](t),z[1,1](t)],[z[2,0](t),z[2,1](t)]]

 > restart;
 > with(IntegrationTools):with(Physics):
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 > h1 := (m,n)->(n+1/2)*KroneckerDelta[n,m];
 (1)
 > h2 := (mu,nu,m2,l)->-(nu*Pi/l)^2/(2*m2)*KroneckerDelta[mu,nu];
 (2)
 > v1 := (m,n,m1)->sqrt(min(n,m)!/max(n,m)!)*(2*m1)^(-abs(n-m)/2)*exp(-1/(4*m1))*LaguerreL(min(n,m),abs(n-m),-1/(2*m1));
 (3)
 > v2 := (mu,nu,l)->4*Pi^2*l*mu*nu*(exp(l/2)-(-1)^(mu+nu)*exp(-l/2))/((Pi*(mu+nu))^2+l^2)/((Pi*(mu-nu))^2+l^2);
 (4)
 > h:=(m,n,mu,nu,m1,m2,l)->evalf(h1(m,n)+h2(mu,nu,m2,l)+v1(m,n,m1)+v2(mu,nu,l));
 (5)
 > m1:=1:m2:=1:l:=1:
 > H:= (m,n,mu,nu)->h(m,n,mu,nu,m1,m2,l);
 (6)
 > H(1,1,0,0);
 (7)
 > eq1:= diff(z(m,nu,t),t)=-I*Sum(Sum(H(m,n,mu,nu)*z(n,mu,t),n=1..N),mu=0..M);
 (8)
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 > zint := Array([[1,0],[0,1]]);
 (9)
 > Z:= Array(1..2,1..2);  for i from 1to 2 do     for j from 1 to 2 do         Z[i,j]:= dsolve({eq1,zint[i,j]},numeric,output=listprocedure);     end do; end do;
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