Ch 2.2: Separable Equations
sTil-{his-ééciilsiégéiiééééiags Eriiééfaid'SIIIiHeéin
rst erder equatiens. Censider the rst erder equatien
_
dx lmy)
ii We can rewrite this in the form
M(x,y)+N(x,y)% : 0
ii Fer example, letM(x,y) = -f(x,y) and N (x,y) = 1.
MATH151 (Spring 2011) Tutorial Notes 9
You can nd more detailed examples in the following online notes by Paul Dawkins: Series Solutions.
The following problems are based on the 8th edition of Boyce and DiPrimas Elementary dierential equations
and boundar
MATH151 (Spring 2011) Tutorial Notes 6
You can nd more detailed examples in the following online notes by Paul Dawkins:
Reduction of Order, Fundamental Sets of Solutions;
Nonhomogeneous Dierential Equations, Undetermined Coecients.
The following problems
MATH151 (Spring 2011) Tutorial Notes 8
You can nd more detailed examples in the following online notes by Paul Dawkins: Review of Power Series.
The following problems are based on the 8th edition of Boyce and DiPrimas Elementary dierential equations
and b
MATH151 (Spring 2011) Tutorial Notes 7
You can nd more detailed examples in the following online notes by Paul Dawkins: Variation of Parameters.
The following problems are based on the 8th edition of Boyce and DiPrimas Elementary dierential equations
and
MATH151(Spring 2011) Tutorial Notes 4
Based on the 8th edition of Boyce and DiPrimas Elementary dierential equations and boundary value
problems, Wiley.
Exercise 3.1: 3, 7, 21, 24
In
3.
7.
Sol:
3.
each of Problems 1 through 7 nd the general solution of th
MATH151 (Spring 2011) Tutorial Notes 10
You can nd more detailed examples in the following online notes by Paul Dawkins: Euler Equations.
The following problems are based on the 8th edition of Boyce and DiPrimas Elementary dierential equations
and boundar
MATH151(Spring 2011) Tutorial Notes 2
Based on the 8th edition of Boyce and DiPrimas Elementary dierential equations and boundary value
problems, Wiley.
Exercise 1.3:
Problems 1 6.
In each of Problems 1 through 6 determine the order of the given dierentia
MATH151(Spring 2011) Tutorial Notes 3
Based on the 8th edition of Boyce and DiPrimas Elementary dierential equations and boundary value
problems, Wiley. Some problems below are only for your reference and will not be discussed in
tutorial class since the
MATH151 (Spring 2011) Tutorial Notes 5
I will use some online notes of Paul. You can download them as follows
http:/tutorial.math.lamar.edu/Classes/DE/IntroSecondOrder.aspx
Second Order Differential Equations
In the previous chapter we looked at first ord
Ch 3.5: Nonhomogeneous Equations;
Method of Undetermined Coefficients
== Recall the nonhomogeneous equation
y" + MD) + 9(0)) = 30)
where p, g, g are oontinuous funotions on an open interval 1.
i: The assooiated homogeneous equation is
y" + 39(3))»r + 9(0
Ch 6.5: Impulse Functions
#1 In seme applieatiens, it is neeessary te deal with phenemena ef
an impulsive nature.
== Fer example, an eleetrieal eireuit er meehanieal system subj eet
to a sudden voltage or force g) of large magnitude that acts
ever a sh
Math151(Spring 2011) List of Suggested Problems
Exercise 1.2:
3. Consider the dierential equation
dy/dt = ay + b,
where both a and b are positive numbers.
(a) Solve the dierential equation.
(b) Sketch the solution for several dierent initial conditions.
(