ENGM 2022 Study Guide - Midterm Guide: Integrating Factor, Stationary Point, List Of Lakes By Volume

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

Document Summary

Thursday, 24 september 2015 (1) [11] find an explicit solution to the following initial-value problem. v(cid:48) = cos(t)v2 , v(0) = 1. Its only stationary point is v = 0. 1 v2 dv = cos(t) dt , (cid:90) 1 (cid:90) whereby v2 dv = By integrating both sides we nd that cos(t) dt . = sin(0) + c , whereby c = 2. This can be solved explicitly to obtain v = . We see that the interval of de nition of this solution is ( , ). You were not asked for this, but you might have been. (2) [11] find an explicit solution to the following initial-value problem. w(cid:48) + 3x2w = e x3 , w(0) = 5 . Its coe cient 3x2 and forcing e x3 are both continuous everywhere. Therefore interval of de nition for each solution is ( , ). (you were not asked for this, but you might have been. )