System of linear differential equations

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For a system of linear differential equations with constant coefficients with known initial conditions an analytical solution can be found.
I however have a system of linear differential equations, where the coefficients are timedependent with the dependence of the coefficients being α_n(t)=exp(k*n*t). Is such a system solvable in general? If I need to be more specific let me know and I will write down the exact system, but for now is there anything general to say?
 
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