Question: how to dsolve to a solution in terms of a number of specified function?

A system of differential equations

But solution I want to express in terms of other specified function

How to dsolve to get a solution that in terms of a list of specified function? For example in terms of sin , cos , Bessel etc ?

Sol := [a(t) = sin(t) + cos(t) , b(t)= sin(t) ....]

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