First Order Difference Equations
Differential equation are great for modeling situations where there is a continually changing
population or value. If the change happens incrementally rather than continuously then
differential equations have their shortco
MATH 204 PRACTICE EXAM I
Please work out each of the given problems on your own paper. Credit will be
based on the steps that you show towards the final answer. Show your work.
Problem 1
Solve the following differential equations.
A. (25 points)
x+y
y' =
Separable Differential Equations
Definition and Solution of a Separable Differential Equation
A differential equation is called separable if it can be written as
f(y)dy = g(x)dx
Steps To Solve a Separable Differential Equation
To solve a separable differe
Modeling with First Order Differential Equations
Whenever there is a process to be investigated, a mathematical model becomes a possibility.
Since most processes involve something changing, derivatives come into play resulting in a
differential equation.
First Order Linear Differential Equations
In this section we will concentrate on first order linear differential equations. Recall that this
means that only a first derivative appears in the differential equation and that the equation is
linear. The gener
Name
MATH 204 PRACTICE FINAL
Please work out each of the given problems on your own paper. Credit will be based on the steps
that you show towards the final answer. Show your work.
Problem 1
Solve the following differential equations.
A. (x2 + 1)y' + 4xy
A Sketch of the Proof of the Existence and Uniqueness
Theorem
Recall the theorem that says that if a first order differential satisfies continuity conditions, then
the initial value problem will have a unique solution in some neighborhood of the initial v
Autonomous Equations and Population Dynamics
Definition
A differential equation is called autonomous if it can be written as
dy/dt = f(y)
Notice that an autonomous differential equation is separable and that a solution can be found by
integrating
Since th
Exact Differential Equations
Consider the equation
f(x,y) = C
Taking the gradient we get
fx(x,y)i + fy(x,y)j = 0
We can write this equation in differential form as
fx(x,y)dx+ fy(x,y)dy = 0
Now divide by dx (we are not pretending to be rigorous here) to ge
Differences Between Linear and Nonlinear Equations
In this section we compare the answers to the two main questions in differential equations for
linear and nonlinear first order differential equations.
Recall that for a first order linear differential eq
Classification of Differential Equations
Recall that a differential equation is an equation (has an equal sign) that involves derivatives.
Just as biologists have a classification system for life, mathematicians have a classification
system for differenti
MATH 204
Differential Equations
Mon, Tues, Wed, and Thurs 1:00 to 2:35 AM
Room D108 (MW) B107 (TTh)
5 UNITS
Instructor: Larry Green
Phone Number
Office: 541-4660 Extension 341
Internet e-mail:.greenl@ltcc.edu
Home Page: http:/www.ltcc.edu/depts/math/
Your