Math 216
July 8, 2015
Review Sheet
Exam 1 is Wednesday, July 15. The following is a list of the topics which you may expect
to appear on the exam:
1. Fundamentals of Differential Equations
2. First Order Differential Equations
a) Separable
b) Homogeneous
EquationsOfFluidMechanics
P2+V222+gZ2+Loss=P1+V122+gZ1+WShaft net in P2+V222+gZ2=P1+V122+gZ1+WShaft net in- Loss WShaft, net in=WPump-WTurbine P2+V222+gZ2=P1+V122+gZ1+WPump-WTurbine- Loss P2+V222+gZ2+WTurbine+ Loss=P1+V122+gZ1+WPump
Energy Equations in te
Math 216 Study Guide for Midterm 1 (Sections 1.1 2.7)
Draw a field for the given differential equation.
1. y ' y 2
2. y ' y ( y 2)
2
Find the solution of the given initial value problem.
3. y ' 2 y te 2t ; y (1) 0
4. ty ' 2 y 4t 2 ; y (1) 2
Find the solut
Math 216 Study Guide for Midterm 2 (Sections 2.9, 4.1 4.6)
1. Sketch the graph of f ( y ) verses y , determine the critical (equilibrium) points, and
classify each one as asymptotically stable, unstable, or semi-stable. Draw the phase line,
and sketch sev
Math 216 Final Study Guide Winter 2015
1. Find the solution of the given initial value problem.
y ' 4 y t 2 3e t , y (0) 0, y ' (0) 2
Use the method of variation of parameters to find a particular solution of the given
differential equation.
2. y ' 4 y 3