Problem 1 This problem provides practice with power series for analytic solutions of analytic Initial-Value Problems. The phase y in a super-conducting Josephson junction (SJJ) evolves with derivatives s' and '" relative to a dimensionless time t =w.t according to the equation [1, Eq. (1), p. 87] 1 + 6 + sin(6) Text Ic' (1) VB where Iext is a current applied externally and I, is a critical current that depends on the junction, so that their ratio Iext/I. is dimensionless, whereas B is the Stewart-McCumber damping parameter. To simplify notation, define K= 1 VB' L= Text Ic (2) The differential equation becomes 6" + K:+ sin (4) = l. (3) (1.1) Show that if |u