ENGM 2022 Study Guide - Midterm Guide: Wronskian, Matlab, Gravitational Acceleration

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

Document Summary

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 . (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. What is w [z1, z2](t)? (3) show that the functions x1(t) = cos(t), x1(t) = sin(t), and x3(t) = 1 are linearly independent. (4) let l be a linear ordinary di erential operator with constant coe cients. Suppose that all the roots of its characteristic polynomial (listed with their multiplicities) are. Give a general real solution for each of the following equations. (a) d2u + 4du + 5u = 3 cos(2t) (b) d2x x = t et (c) d2y y =