ENGM 2022 Study Guide - Midterm Guide: System Of Linear Equations, Parameterized Complexity, Gravitational Acceleration

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

Document Summary

Thursday, 22 october 2015 (1) [4] give the interval of de nition for the solution of the initial-value problem w(cid:48)(cid:48)(cid:48) 5 t w(cid:48) + cos(5t) The equation is linear and is already in normal form. The coe cient of w(cid:48) is unde ned at t = 0 and is continuous elsewhere. The coe cient of w is unde ned at t = 2 and is continuous elsewhere. The forcing is unde ned at t = 4 and is continuous elsewhere. There are 12 roots listed above, so the degree of the characteristic polynomial is 12, whereby the order of l is also 12. A general solution is v(t) = c1e 2t cos(5t) + c2e 2t sin(5t) + c3t e 2t cos(5t) + c4t e 2t sin(5t) + c5 cos(4t) + c6 sin(4t) + c7e3t + c8te3t + c9t2e3t + c10 + c11t + c12t2 . Suppose you know that w [x1, x2, x3](0) = 5.