Math 208 - Exam 2, March 17, 2009
Name:
Key
Problem 1. Find the general solution on R to each of the following dierential equations:
(a). y (4) + 2y + y = 0.
(b). y (4) 8y + 16y = sin t + e2t .
(c). y
Math 208 - Exam 3, April 14, 2009
Name:
Key
Problem 1 (20 points). Find the general solution to the dierential equation y + xy = 1 + x in powers of
x. You may leave your answer in the form of a recurr
Jenny Gilbert
MATH 208-01
Final Review Outline: Major Goals in Differential Equations
Goal: Be able to define and understand differential equations, associated terminology,
and real-life applications
Jenny Gilbert
MATH 208-01
Midterm Review
Outline: Major Goals in Differential Equations
Be able to define and understand differential equations, associated terminology, and reallife applications
o Di
Math 208 - Quiz 10, April 9, 2009
Name:
Key
Problem 1. Use the Laplace transform to solve the initial value problem: y 4y + 4y = 0, y (0) = 1, y (0) = 1.
Solution 1. By using the formula Lcfw_f (n) (t
Math 208 - Quiz 9, April 2, 2009
Name:
Key
Problem 1. Find the general solution to the dierential equation x2 y 3xy + 4y = 0, for x > 0.
Solution 1. We rst look for a solution of the form y (x) = xr f
Math 208 - Quiz 8, March 26, 2009
Name:
Key
Problem 1. Find a recurrence relation for the coecients in a power series solution to dierential equation y + y
xy = 0 about the point x0 = 0. Use this to
Math 208 - Quiz 7, March 12, 2009
Name:
Key
Problem 1. Find the general solution on R to the dierential equation y (6) y = 0.
Solution 1. The characteristic polynomial to this equation is r6 1. To nd
Math 208 - Quiz 6, February 26, 2009
Name:
Key
Problem 1. Find the general solution on R to the dierential equation y 2y + y = et .
Solution 1. First of all note that the characteristic polynomial of
Math 208 - Quiz 5, February 19, 2009
Name:
Key
Problem 1. Find a solution on R to the dierential equation y + 2y + 5y = 0 subject to the initial conditions
y (0) = 1, y (0) = 0.
Solution 1. The charac
Math 208 - Quiz 4, February 5, 2009
Name:
Key
Problem 1. Find the solution to the dierential equation (2y sin x ex sin y ) + (ex cos y 2 cos x)y = 0.
Solution 1. This dierential equation is of the for
Math 208 - Quiz 3, January 29, 2009
Name:
Key
Problem 1. A large tank is half full with a mixture of salt dissolved in water. Pure water is pumped into the tank
at the rate of 3 gallons per minute, an
Math 208 - Quiz 1, January 15, 2009
Name:
Key
Problem 1. Solve each of the following initial value problems and graph the solution.
(a).
dy
dt
= y + 3, y (0) = 2.
(b).
dy
dt
= 2y + 1, y (0) = 1.
(c).
Section 9.4: Systems of Linear Differential Equations
Normal Form, Fundamental Solution Set, Fundamental Matrix
o Normal Form
Homogenous when , otherwise it is nonhomogeneous
o Fundamental Solution