UTSA, Math 3613 003, Differential Equations I
Fall Semester, 2014
Homework 1
Due October 23, 2014
Dr. Ivanka Stamova
Instructor:
Student Name: …………………………………………………
1. (5 points) Solve the differential equations:
(a) y" 2 y' y
(c) y" y
(e) y ( IV )
3е
x
x 1;
(b) y" y
(d) y" ( y ) 2
sin x cos 2 x ;
2y
e2x
ex
2e
y
;
cos x
y
2. (5 points) Solve the initial value problems
(a) xy" y ' , y (1)
(b) y" 4 y
12 x 2
6y
2 x 2 , y (0)
x 2e
(c) y" 2 y' 2 y
(d) y
0 , y (1) 1
12 y
x
Total: 10 points
cos x , y(0)
8y
(e) y" 2( y' ) 3 y , y (0)
0 , y (0) 1
3e
2x
y (0)
, y (0)
0 , y (0) 1
0
0 , y (0)
y (0) 1
x;

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