Homework 1 (MATH 2310-04)
Name (Print):
Due date: Thursday, Feb. 6, 2014
1. Find the general solution of the given differential equation, and use it to determine how
solutions behave as t :
t
dy
2 y sin( t ), t 0
dt
Solution: y( t ) cos( t ) sin( t ) C
t
Homework 3 (MATH 2310-04)
Name (Print):
Due date: Thursday, Feb. 20, 2014
1. Determine whether the following differential equation is exact. If it is exact, find the
solution.
y
dy
6x ln(x ) 2
0.
x0
x
dx
y
Solution : This equation is exact :
C 3x 2
ln (
Homework 2 (MATH 2310-04)
Name (Print):
Due date: Thursday, Feb. 13, 2014
1. Solve the given differential equations:
a)
b)
dy
y 2 sin( x ) 0
dx
dy
x2
dx y(1 x 3 )
Solution: a )
y( x ) 1 /(C cos( x )
b)
y( x ) (2 ln 1 x 3 / 3 C)1/ 2
2. Solve the following
Homework 9 (MATH 2310-04)
Name (Print):
Due date: April 19, 2012
1. Use the Laplace transform to solve the given initial value problem.
5
y' ' y' y f ( t ),
4
y(0) 0,
0t
t
sin( t )
y' (0) 0, f ( t )
0
Solution :
y(t) = h(t) + u h(t )
h(t) = (4/17) [4 cos
Homework 8 (MATH 2310-04)
Name (Print):
Due date: April 23, 2013
1. Find the inverse Laplace transform of the given functions (you may need partial
fractions for doing this).
3s
s s6
2
b) F(s) 2
s 3s 4
8s 2 4s 12
c) F(s)
s(s 2 4)
a ) F(s)
2
Solution :
a
Homework 6 (MATH 2310-04)
Due date: Tuesday, March 26, 2013
Name (Print):
1. Use the method of reduction of order to find a second solution of the given differential
equation.
t 2 y' '4 ty'6 y 0, t 0
Solution :
y1 ( t ) t 2 .
y( t ) c1t 2 c 2 t 3
2. Use t
Homework 7 (MATH 2310-04)
Due date: Tuesday, April 2, 2013
Name (Print):
1. Consider the following differential equation.
2 y' '4 y'6 y 6e 2 t .
a) Use the method of undetermined coefficients to find the general solution.
b) Calculate the solution for the