MATH 2341 Study Guide - Final Guide: Saddle Point, Jacobian Matrix And Determinant, Phase Plane
9 Jan 2019
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Put your nal answers to each question in the designated spaces. A calculator and a single sheet of formulas are allowed. Show your work: 10 points solve the following initial value problems. (a) (1 + 2t) dy dt. = 1 + y2, y(0) = 0. (b) dy dt. Spring 2013: 8 points consider the initial-value problem dy/dt = y3, y(0) = Spring 2013: 12 points an 80 gallon tank initially contains 20 gallons of pure water. Spring 2013: 10 points solve the following initial value problems. (a) y y = et, y(0) = 0, y (0) = 0 (b) y + y = et, y(0) = 0, y (0) = 0. Spring 2013: 8 points consider the linear system y = ay, with a =(cid:18) 1. 1 (a) it turns out that a has a single eigenvalue, . compute this eigenvalue. (b) given the initial condition v0 =(cid:18)2.
