M302 Hw3 (S. Zhang) 3.3, 3.4, 3.5
2. (3.4:24)
t2 y + 2ty 2y = 0, y1 = t
0. 3.3: 4-6,14-18
1. (3.3:6)
Use the method of reduction to solve
Write the number in a + bi form:
ans:
1+2i
y2 = vy1 = vt
ans:
By the DE
1+2i = e ln +i2 ln =
2. (3.3:18)
1
(cos(2 ln
M302 Hw4 (S. Zhang) 3.6, 3.7, 3.8
u2 = 4t
0. 3.6: 3-6, 10, 13-14
u1 = u2 t = 4t
1. (3.6:4)
Find the general solution. Here you need to nd
yp twice, by both the method of undetermined coecients
and the method of variation of parameters.
u1 = 2t2
4y 4y + y
M302 Hw2 (S. Zhang) 2.4,3.1,3.2
0. 3.1: 1-3,8-9,12,21,22
1. (3.1:8)
0. 2.4: 2-4, 8-9, 13,15,21
Find the general solution:
1. (2.4:4)
Determine an interval in which the solution is
certain to exist (without solving the problem)
y 2y 2y = 0
ans:
(4 t2 )y +
M302 Hw1 (S. Zhang) 2.1-2.3
2.1: 1-2, 14-16, 30-31
0.
1.2
99
1.
1.2
31
y =1
=e3t (
(2.1:1)
Draw direction eld. Describe how solutions
behave for large t. Solve the equation and determine how
solutions behave for large t.
e3t t +
et )
1
1
=e3t ( e3t t e3t
M302 Study Guide 1 (S. Zhang)
y =1
1. (2.1:1)
Draw direction eld. Describe how solutions behave for large t. Solve the equation and determine how
solutions behave for large t.
=e3t (
ans:
Or a simpler answer that as 1 t ,
3
(0, 1)
2
y ,
2. (2.1:15)
when t
11. (2.4:13)
Solve the problem and nd an interval in which
the solution exists
M302 Study Guide 1 (S. Zhang)
1. (2.1:1)
Draw direction eld. Describe how solutions behave for large t. Solve the equation and determine how
solutions behave for large t.
y = 4