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Math 2214 Practice Test 1 Fall, 2014

1.

Solve the initial value problems.

(a)

1

2 8, (0) 2y y y! + = =

(b)

3, (1) 2ty y t y! + = = "

(c)

2(1 ), (4) 0yy t y y! = " =

(d)

21, (1) 12ty y e y

t

!" + = =

(e)

( 1) , (ln 2) 1ty t y t y! + + = =

(f)

4 44 1, (0) 2t te y e y y! + = =

(g)

, (0) 0y ye y te t y!" = =

2. (a) Find all equilibrium solution(s), if any, of the differential equation2( 4)

.1

t yy

y

!" =

+

(b)On what intervalt! does the existence-uniqueness theorem guarantee a unique solution for the

initial problem:cos

(2 1) , (1) 03

y tt y y

t t!+ " = =

"

3. Consider the following initial value problem:3 2( 1) 0, (0) 1t yy t y!+ + = =

(a) Find the biggest open rectangle (a t b