Differential Equations
Preface
Here are my online notes for my differential equations course that I teach here at Lamar University. Despite the fact that these are my class notes they should be accessible to anyone wanting to learn how to solve differenti
Math 3301
Homework Set 2 Solutions
10 Points
#1. (3 pts) Not much to do here for the solution.
e
4 y -1
dy = 1 - 2 x dx
1
4
e 4 y -1 = x - x 2 + c
Now, apply the initial condition to get,
c = 1 e15
4
1
4
e 4 y -1 = x - x 2 + 1 e15
4
y ( x ) = 1 1 + ln ( e
Math 3301
Homework Set 3 Solutions
10 Points
#1. (3 pts) Ill use weeks as the time frame for my solution(s). Here are the IVPs for this problem.
P = rP
P ( 0 ) = 200
P (12 ) = 400
P1 = rP1 + 15 - 35 = rP1 - 20
P1 ( 0 ) = 200
P2 = rP2 + 20 - 25 = rP2 - 5
P
Math 3301
Homework Set 5 Solutions
#1. (3 pts) y2 ( x ) = x v ( x )
y2 = v + x v
10 Points
y2 = 2v + x v
3x 2 ( 2v + x v ) - 2 x ( v + x v ) + 2 ( x v ) = 0
3 x3v + ( 6 x 2 - 2 x 2 ) v + ( -2 x + 2 x ) v = 0
3 x3v + 4 x 2 v = 0
Letting w = v and doing a l
Math 3301
Homework Set 6 Solutions
10 Points
#2. (2 pts) Ill leave it to you to verify that the complimentary solution is : yc ( t ) = c1 + c2e 4 t
The guess for the particular solution and its derivatives are,
YP = Ae 7 t + t ( Bt 2 + Ct + D )
YP = 7 Ae
Math 3301
Homework Set 7 Solutions
10 Points
#2. (2 pts) This one is really just the same as #1 except it is going to involve two integrals/limits to deal
with. Here is the work for this problem,
L cfw_4e -7 t + e3t =
0
( 4e
-7 t
+ e3t ) e- st dt = 4e-7
Math 3301
Homework Set 8 Solutions
10 Points
#3. (3 pts) We first need to get the function written in terms of Heavisides and properly shifted.
h ( t ) = -4 + (10t + 4 ) u3 ( t ) + ( 6 - 10t ) u8 ( t )
= -4 + (10 ( t - 3 + 3) + 4 ) u3 ( t ) + ( 6 - 10 ( t
Math 3301
Homework Set 9 Solutions
10 Points
#2. (3 pts) First take the transform of everything, plug in the initial conditions and solve for Y ( s ) .
8 5e -10 s
4 ( s 2Y ( s ) - sy ( 0 ) - y ( 0 ) ) - 4 ( sY ( s ) - y ( 0 ) ) + Y ( s ) = + 2
s
s
8 5e -1
Math 3301
Homework Set 10 Solutions
10 Points
#7. (3 pts) Ill leave it to you to verify that the eigenvalues and eigenvectors for this matrix are,
l 1 = -4
-5
r
h (1) =
3
l 2 = -2
-1
r
h ( 2) =
1
The general solution is then,
-5
-1
r
x ( t ) = c1
Math 3301
Homework Set 1 Solutions
10 Points
#1. (2 pts) The derivative will be zero at y = -3 ,
y = 0 and y = 4 . A sketch of the direction field
and some solutions is to the right. From this we
can see the long term behavior and dependence
on y ( 0 ) .
Differential Equations
Preface
Here are my online notes for my differential equations course that I teach here at Lamar University. Despite the fact that these are my class notes they should be accessible to anyone wanting to learn how to solve differenti
Differential Equations
Preface
Here are my online notes for my differential equations course that I teach here at Lamar University. Despite the fact that these are my class notes, they should be accessible to anyone wanting to learn how to solve different
Differential Equations
Preface
Here are my online notes for my differential equations course that I teach here at Lamar University. Despite the fact that these are my class notes, they should be accessible to anyone wanting to learn how to solve different
Differential Equations
Preface
Here are my online notes for my differential equations course that I teach here at Lamar University. Despite the fact that these are my class notes they should be accessible to anyone wanting to learn how to solve differenti
Differential Equations
Preface
Here are my online notes for my differential equations course that I teach here at Lamar University. Despite the fact that these are my class notes they should be accessible to anyone wanting to learn how to solve differenti
Differential Equations
Preface
Here are my online notes for my differential equations course that I teach here at Lamar University. Despite the fact that these are my class notes, they should be accessible to anyone wanting to learn how to solve different
Differential Equations
Preface
Here are my online notes for my differential equations course that I teach here at Lamar University. Despite the fact that these are my class notes they should be accessible to anyone wanting to learn how to solve differenti
Differential Equations
Preface
Here are my online notes for my differential equations course that I teach here at Lamar University. Despite the fact that these are my class notes they should be accessible to anyone wanting to learn how to solve differenti
Differential Equations
Preface
Here are my online notes for my differential equations course that I teach here at Lamar University. Despite the fact that these are my class notes, they should be accessible to anyone wanting to learn how to solve different
Differential Equations
Preface
Here are my online notes for my differential equations course that I teach here at Lamar University. Despite the fact that these are my class notes they should be accessible to anyone wanting to learn how to solve differenti
Differential Equations
Preface
Here are my online notes for my differential equations course that I teach here at Lamar University. Despite the fact that these are my class notes, they should be accessible to anyone wanting to learn how to solve different
Differential Equations
Preface
Here are my online notes for my differential equations course that I teach here at Lamar University. Despite the fact that these are my class notes they should be accessible to anyone wanting to learn how to solve differenti
Differential Equations
Preface
Here are my online notes for my differential equations course that I teach here at Lamar University. Despite the fact that these are my class notes they should be accessible to anyone wanting to learn how to solve differenti
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