MAT 274 TEST 1
Instructor : Dongrin Kim Name : Score :
1. Find an integrating factor for the linear differential equation ty + (t + 1)y = t, t > 0. Ans : tet
2. Find the general solution for y + (2/t)y = (cos t)/t2 . Use the integrating factor (t) =
 CHAPTER 2. 
Chapter Two
Section 2.1 1a+b
a,b Based on the direction field, all solutions seem to converge to a specific increasing function. a b The integrating factor is .a>b oe /$> , and hence Ca>b oe >$ "* /#>  /$> It follows that all s
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MAT 274 TEST 2
Instructor : Dongrin Kim Name : Score :
1. Find the general solution of each differential equation. (a) y + 3y + y = 0 Ans : c1 e(3+
5)t/2
+ c2 e(3
5)t/2
(b) y  8y + 16y = 0 Ans : c1 e4t + c2 te4t
(c) y + 4y + 8y = 0 Ans : c1
MAT 274 TEST 3
Instructor : Dongrin Kim Name : Score :
1. Find the radius of convergence of the power series
n=0
(1)n n2 (x + 2)n . 3n
Ans : 3
2. Determine the Taylor series about the point x0 . Also determine the radius of convergence of the s