Review for rst test, Math 320
(1) Solve the initial value problem
1 + y2
, y (0) = 0.
1+t
Find the largest interval on which the solution exists.
(2) Consider the initial value problem
y=
(t + 1)y y = t,
y (0) = 1.
(a) By applying the existence and unique
Introduction to Ordinary Dierential Equations 320 Review
1. Find the general solution of the dierential equation
y (4) + 2y + y = 0.
2. Find the general solution of the dierential equation
y (4) + 2y + y = 3 + 2 cos t.
3. Find the general solution of the
Dierential Equations, Math 320
Homework 1
1. Solve the initial value problem
y+t
y=
, y (1) = 0.
t
Find the existence interval.
Solution: The integrating factor is 1/t
1
y
t
1
=.
t
Therefore,
1
y = ln t + c
t
and
y (t) = t ln t + ct.
From the initial cond
Homework 2, Math 320
1. Find the equilibrium solutions of the dierential equation
y = y 2 (y 2 4y + 3)
and classify according to stable and unstable solutions. Draw the phase line.
Solution: The zeros of f (y ) = y 2 (y 2 4y + 3) = 0 are y = 0, 1, 3, so
t
Homework 3, Math 320
1. Find a fundamental set of solutions for the dierential equation
y (4) 4y + 7y 6y + 2y = 0.
Solution: The characteristic equation is
0 = r4 4r3 + 7r2 6r + 2 = (r2 2r + 2)(r 1)2 .
The solutions are r = 1, 1, 1 + i, 1 i. A fundamental
Homework 4, Math 320
1. Find all singular points of the dierential equation
x(x2 1)y + 2x(3 + x)y 2y = 0.
At each regular singular point nd the indicial equation and the corresponding solutions r1 , r2 .
Solution: The equation has three singular points x
Midterm Exam, Math 320, October 21, 2008
(1) Solve the initial value problem
yy = et ,
y (0) = 1.
Find the largest interval on which the solution exists.
Solution: This is a separated dierential equation. The solution is found
by
et dt
y dy =
so
12
y = et
MATH 230 INTRODUCTORY STATISTICS:
This course does meet the Natural Sciences and Mathematics Non-Laboratory (GM)
(GM) general requirements at UW-Whitewater.
All successfully completed PIE courses received college credit at the University of WisconsinWhite