# Solve differential equation system for HIV treatment model?

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 Dear All, I was working on a project about optimal strategies for HIV treatment, models used from [Butler, Kirschner, and Lenhart] 1997. This model explains the spread of HIV viruses in the human body, where there is one control function u(t).My work is following pontryagin maximum principle. But i have a problem solving the differential equation system, where there are 6 differential equations with 6 initial conditions. Here i use software Mathematica 11 when I execute the code there is no error that appears and he just returning DSolve code that i write. DSolve[{eq1, eq2, eq3, eq4, eq5, eq6, T[0] == 800, Ti[0] == 0.04, V[0] == 1.5, l1[20] == 0, l2[20] == 0, l3[20] == 0}, {l1[t], l2[t], l3[t], T[t], Ti[t], V[t]}, t] I cannot guarantee that the analytical solution exists, but is there something wrong with code I wrote? Or is there an alternative solution to complete the differential equation system?I hope you are pleased to check the file that I attached.Many thanks . Attachments: