Math 1270 Spring 2013
Homework #2
Due Friday, January 25
Problem 1: Solve the initial value problem
(a)
y 2t /( y t 2 y) ,
y(0) 2
(b)
(c)
y y 2 sin t 0 ,
y
2
dy
x
,
x 1 dx 4 y
2
y( / 2) 1
y(0) 1 / 2
Problem 2: State where in the ty-plane the hypotheses of
MATH 1270: Spring 2013
Exam I Review Topics
Reading: Chapters: 1.1-1.3, 2.1-2.3, 2.5-2.7, 8.1-8.2, 3.1-3.8
Theory:
Definition of an ordinary differential equation, order, initial condition, solution
Definition of a linear and nonlinear ODE
Definition o
Homework 2 for grading, hint}: 0292, Spring 2016
Due: Monday. Fnbnmry 22, 2016
Show all the necessary steps to receivm full credit.
I. Find The gmmml salutinn m Eﬂfh one if the iollnwing 00133:
[III [5 paints} y” + y' — my =r {J
21+A§42=0
0+4)(9c—s)=-0
2.
Review Exam 1, Math 0202, Spring 2016
1. Solve the differential equation y 0 3y = 5 by the method of variation of parameters.
2. Solve the differential equation y 0 3y = 5 by the method of the integrating factor.
3. On the day of his birth, Jasons grandmo
Math 1270 Spring 2013
Homework #4
Due February 8
Problem 1: Solve the given differential equation or initial value problem using an appropriate
method.
dy
2x y
(a)
,
y(0) 0
dx 3 3 y 2 x
(c)
dy
y ye x
dx
(2 y 3x)dx xdy ,
(d)
(e)
y e x y
2 sin y cos xdx co
Math 1270 Spring 2013
Homework #5
Due February 15
Problem 1: Find the solution of the given initial value problem. Sketch the graph of the
solution and describe its behavior as t increases.
(a)
y 4 y 3 y 0 ,
y (0) 2 ,
y (0) 1
(b)
6 y 5 y y 0 ,
y (0) 4 ,
y
Math 1270 Spring 2013
Homework #6
Due February 22
Problem 1: Determine whether the equation is exact. If so, solve the equation
(a)
xy (cos x) y (sin x) y 0 , x 0
Problem 2: If the Wronskian of any two solutions of y p(t ) y q(t ) y 0 is constant,
what do
Math 1270 Spring 2013
Homework #7
Due March 22
Problem 1: Determine whether the vectors are linearly independent. If they are linearly
dependent, find a relation among them (i.e., find constants c1 , c2 , c3 , c4 , not all of which
are zero, such that c1x