Please help with this differential equation problem:

Let us consider an aging spring - mass system where the restoring force of the spring and the damping force are both weakening exponentially over time. Let the equation of motion of the mass be governed by the following initial value problem: 211," (t) + Ze'o'ltu' (t) + 4602% (t) = 0, u(0) = 1, u' (0) = 0 M Using what you have learned in this module, nd the rst four nonzero terms in the series solution of the above IVP about t = 0. You may use following facts: At \" . o e)\" = 23::0 (n!) (Standard Taylor Series of e\" aboutt,L : 0) (2:020 ant") (22:0 but\") = 2:020 out\" ,where on = (10 b", + a1 bn_1 + - - - + limbo (Rule for multiplying two series)