questions below:

m = 2 kg and a damping constant b = 1 N-sec/m with initial conditions x(t)) = 4 m and x'(0) = 0 m/sec, then the displacement x(t) is governed by the initial value problem 2x\"(t) + x'(t) + (7 - t)x(t) = 0; x(0) = 4, x'(0) = 0. Find the rst four nonzero terms in a power series expansion about t = 0 for the displacement. As a spring is heated, its spring \"constant" decreases. Suppose the spring is heated so that the spring "constant" at time t is k(t) = 7 -t Nlm. If the unforced mass-spring system has mass k0) : 7: 1 N / I 'SGC I11 x(t) x(0) = 4 x'(0) = 0 x(t) = + (Type an expression that includes all terms up to order 4.) Find the first four nonzero terms in a power series expansion about x = 0 for a general solution to the given differential equation. (x2 + 19) y" + y= 0 (. . . y(x) = 1 + ... (Type an expression in terms of an and a, that includes all terms up to order 3.)