Differential Equations I

UTSA, Math 3613 003, Differential Equations I Fall Semester, 2014 Homework 1 Due October 23, 2014 Instructor: Dr. Ivanka Stamova Student Name: ………………………………………………… 1. (5 points) Solve the differential equations:

(a) 13'2" � �� � xеyyy x ; (b) xeeyy xx �� c� 2" ;

(c) xxyy 2cossin" � � ; (d) yeyy � c� 2)(" 2 ; (e) xyyy IV cos2)( �cc� 2. (5 points) Solve the initial value problems

(a) '" yxy , 0)1( y , 1)1( cy

(b) 22124" 2 �� c� xxyy , 0)0( y , 1)0( cy

(c) xexyyy x cos2'2" 2 � �� , 0)0()0( c yy

(d) xeyyyy 238126 � �c�cc�ccc , 0)0( y , 1)0()0( cc c yy

(e) yyy 3)'(2" , 0)0( y , 1)0( cy

Total: 10 points