ENGM 2022 Study Guide - Midterm Guide: Wronskian, Linear Independence, Matlab

• School: Dalhousie University
• Department: Engineering Mathematics
• Course: ENGM 2022
• Professor: All

Document Summary

Solutions of sample problems for second in-class exam. Math 246, fall 2015, professor david levermore (1) give the interval of de nition for the solution of the initial-value problem d3x dt3 + cos(3t) 1 + t x(2) = x(cid:48)(2) = x(cid:48)(cid:48)(2) = 0 . The coe cient and forcing are both continuous over the interval ( 1, 4), which contains the initial time t = 2. The coe cient is not de ned at t = 4 while the forcing is not de ned at t = 1. Therefore the interval of de nition is ( 1, 4). (2) suppose that z1(t) and z2(t) are solutions of the di erential equation z(cid:48)(cid:48) + 2z(cid:48) + (1 + t2)z = 0 . Suppose you know that w [z1, z2](0) = 5. Abel"s theorem states that w(t) = w [z1, z2](t) satis es w(cid:48) + 2w = 0. Because w(0) = w [z1, z2](0) = 5, we obtain w(t) = 5e 2t.