Question: solutions of IVP in other IVP

sys1:={diff(x1(t),t)=(3+5*I)*x1(t)-sqrt(2)*(cos(3)+I*sin(3))*y1(t)-2*I*z1(t),diff(y1(t),t)=conjugate(x1(t)),diff(z1(t),t)=0.25-0.3*z1(t)-2*I*(x1(t)-y1(t))}:

sys2:={diff(x(t),t)=(3+5*I)*x(t)-sqrt(2)*(cos(3)+I*sin(3))*y(t)-2*I*z(t)-2*I*(cos(5*t)-1)*z1(t),diff(y(t),t)=conjugate(x(t)),diff(z(t),t)=0.25-0.3*z(t)-2*I*(x(t)-y(t))-2*I*(cos(5*t)-1)*(x1(t)-y1(t))}:
 

I  wonder if Maple can solve it. I solve it (by laplace transform)analytically but it consumes time and take time to put in maple in order to plot the solutions. It is too complicated because non-autonomous ODE with complex coeff. further we substitue the solutions of sys1 in sys2 and solve sys2 at the end plot x,y,z.

I get rid of it , realy I need help.