u can solve it by consider each initial condition as a voltage source with value of L*i(0)

Thanks for your answer Mr Adel Dakhil, but this way you have suggested is applied for S-domain calculation.

It is not solvable, since

"series connected" == "same currents"

"different initial" == "different curents"

or I have not understood your question.

Thanks for your answer Mr Simone Orcioni.