Math 46 Practice Final Exam
Dec 7, 2016
NAME (please print):
NetID (please print):
1. Write clearly and show all work.
2. You will be graded for both completeness and correctness for this exam.
3. Thi
Homework 7
Math 046 (020) Introduction to Ordinary Dierential Equations
Due Thursday, December 6 in Discussion
Mathematics Department
University of California, Riverside
Fall Quarter 2012
The Method o
Sample Final
Math 046 (020) Introduction to Ordinary Dierential Equations
Mathematics Department
University of California, Riverside
Fall Quarter 2012
Name:
1. Solve the dierential equation
y 000
2y 0
Sample Midterm
Math 046 (020) Introduction to Ordinary Dierential Equations
Mathematics Department
University of California, Riverside
Fall Quarter 2012
Name:
1. Solve the initial-value problem
y 0 +
Chapter5(continue):ExactEquations,
IntegratingFactors
Consider a first order differential equation of the form
M ( x, y ) N ( x, y ) y0
Suppose there is a function F such that
Fx ( x, y ) M ( x, y ),
Chapter5:ExactFirstOrderDifferential
Equations
Many times, it will be convenient to write a first
order ordinary differential equation in the form
M ( x, y )dx N ( x, y )dy 0.
It is the same as M(x,y)
Chapter11:TheMethodofUndetermined
Coefficients
Let
L( y ) y p( x) y q( x) y,
then the general solution of the equation
L( y ) f ( x) is yh y p ,
where is the general solution of
yha particular solutio
Chapter 9: Second-Order Linear Homogeneous
Differential Equations with Constant Coefficients
Thus far we have concentrated on first-order
differential equations. We will now turn our
attentions to the
Characteristic Equation
In general, to solve the second order equation with constant
coefficients,
ay by cy 0,
we begin by assuming a solution of the form y = ert.
Substituting this into the different
Chapter4:SeparableEquations
A first order equation y=f(x, y) is separable if
f ( x, y ) g ( x) / h( y ).
That is,
h( y )dy g ( x)dx
By integration, we get:
h( y )dy g ( x)dx.
Chapter4:SeparableEquatio
Chapter1:
BasicConcepts
A differential equation is an equation
containing one or more derivatives of an
unknown function.
Example 1:
y ' 5 x 3
e y y"2( y ' ) 2 1
(1.1)
(1.2)
Chapter1:
BasicConcepts
A
Chapter6(continue):BernoulliEquations
Consider a first order differential equation of the form
y ' p( x) y q( x) y r r 1.
We have:
y'
1 r
p ( x) y q( x) or y 0 if r 0.
r
y
Let
z y1 r
then
z '(1 r ) p
Chapter7:Application
GrowthandDecay
One of the most common mathematical
models for a physical process is exponential
model Q=aQ. The rate of change is
proportional to the quantity.
a (t t )
Q
Q
e
.
So
Homework 4
Math 046 (020) Introduction to Ordinary Dierential Equations
Due Thursday, November 1 in Discussion
Mathematics Department
University of California, Riverside
Fall Quarter 2012
Linear First
Homework 6
Math 046 (020) Introduction to Ordinary Dierential Equations
Due Thursday, November 29 in Discussion
Mathematics Department
University of California, Riverside
Fall Quarter 2012
nth-Order L
Math 46 Practice Final Exam Solution
Dec 7, 2016
NAME (please print):
NetID (please print):
1. Write clearly and show all work.
2. You will be graded for both completeness and correctness for this exa
Math 46 Practice Final Exam
Dec 7, 2016
NAME (please print):
NetID (please print):
1. Write clearly and show all work.
2. You will be graded for both completeness and correctness for this exam.
3. Thi
Math 46 Practice Final Exam Solution
Dec 7, 2016
NAME (please print):
NetID (please print):
1. Write clearly and show all work.
2. You will be graded for both completeness and correctness for this exa
Weekly Homework and Reading Assignments for
Math 46 ODE Fall 2017
The weekly reading assignments from Schaums Outlines will parallel the
lecture in class, sometimes giving more explicit, hard-nosed re
* SAMPLE * Math 46 Midterm Fall 2017
Write neatly. Show all your work. No books, notes, or calculators
are allowed.
On the actual midterm, there will be space provided for solving the
problems, so t
Mathematics 46: Practice Problems for Final exam
Winter 2016
Solve the following equations. If there is no initial condition, find the general
solution. If there are initial conditions, solve the init
Mathematics 46: Practice Problems for Final exam
Winter 2016
Solve the following equations. If there is no initial condition, find the general
solution. If there are initial conditions, solve the init
Homework 1
Math 046 (020) Introduction to Ordinary Dierential Equations
Due Thursday, October 11 in Discussion
Mathematics Department
University of California, Riverside
Fall Quarter 2012
Instructions
Homework 2
Math 046 (020) Introduction to Ordinary Dierential Equations
Due Thursday, October 18 in Discussion
Mathematics Department
University of California, Riverside
Fall Quarter 2012
Instructions
Homework 5
Math 046 (020) Introduction to Ordinary Dierential Equations
Due Thursday, November 15 in Discussion
Mathematics Department
University of California, Riverside
Fall Quarter 2012
Linear Dier
Homework 3
Math 046 (020) Introduction to Ordinary Dierential Equations
Due Thursday, October 25 in Discussion
Mathematics Department
University of California, Riverside
Fall Quarter 2012
Instructions
Chapter6:LinearFirstOrderEquations
A first order equation y=f(x, y) is linear if f(x,y)=
-p(x)y+q(x),
i.e., y=-p(x)y+q(x) or y+p(x)y=q(x).
Or
( p ( x) y q ( x)dx dy 0.
We have:
M (linear
x, y )if
p (