Question: How can I solve a set of linear differential equations?

Deal All,

I have a system of linear differential equations with unknown functions T[1](t) to T[n](t). In the attached example, I considered the value of n equal to 10, but depending on the problem, the value of n may be higher. Maple is not able to solve this problem analytically with the ‘dsolve’. 

Does anyone have an idea to analytically solve for such a set of linear differential equations?

Best wishes

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