Consider an initial value problem given a linear differential equation of the form t20 with d’u d'u du -+2. dt +" = 31² – 2e" being given the dt' dt initial conditions u(0) = u'(0) = u"(0) = 0. 1)Obtain the solution of the homogeneous part of the differential equation in question and find the specific solution using the method of uncertain coefficients and write the solution to the related initial-value problem.

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A: Since you have asked multiple question, we will solve the first question for you. If youwant any…