Question: How to verify eq by using (2), (3) and (4)?

How to verify eq by using (2), (3) and (4)? Since lambda's, A's, B's and a are constant, but they appear as variables i.e., D[2](A1)..., (D[2] -> d/dt (derivative w.r.t 't')). Also q(n+1,t)- q(n,t) = a (const). Therefore, d/dt(q(n+1),t) - d/dt,(q(n,t))=0

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