MATH 215 Study Guide - Midterm Guide: Academic Dishonesty, Jacobian Matrix And Determinant, Phase Portrait
Document Summary
I have read and understood the instructions below: No notes or books or calculators are allowed: justify every answer whenever is necessary, and show your work. Unsupported answers will receive no credit: you will be given 2. 5 hrs to write this exam. Cases of academic dishonesty may lead to a zero grade in the exam, a zero grade in the course, and other measures, such as suspension from this university. Problem i. (a) (4 marks) solve the following linear ode: 2 t2 t > 0. (b) (4 marks) solve the following nonlinear ode: (hint: the substitution w = v 1/2 will probably simplify matters) t2w + 2tw w3 = 0, t > 0. Problem ii. (a) (4 marks) find all values of a and b for which the ode below is an exact equation. (it is not necessary to solve the ode. ) [10 marks] ax3ex+y + bx4ex+y + 2x + (x4ex+y + 2y) dy dx.
