Introduction to Modeling with Differential Equations
CHM 220

Fall 2012
Lesson 2: Separable variables
Exercise 2.1.
a2 y 2 dx + (b2 + x2 )dy = 0.
Solution. Multiplying both sides of the equation to
1
(b2 + x2 ) a2 y 2
we have the equation:
dx
dy
+
= 0.
(b2 + x2 )
a2 y 2
Therefore, by formal integrating we obtain
dy
dx
+
= c.
Introduction to Modeling with Differential Equations
CHM 220

Fall 2012
AMA126
Tutorial 2
1. In each of Exercises (a)(g) prove that y is a solution of the
indicated differential equation
a. y=C1ex+C2e2x; y3y+2y=0
b. y=Ce3x; y+3y=0
c. y=ex(C1cosx+C2sinx); y2y+2y=0
d. y=(C1+C2x)e2x; y+4y+4y=0
e. y=Cx2/3; 2xy3dx+3x2y2dy=0
Introduction to Modeling with Differential Equations
CHM 220

Fall 2012
CHM 220 Introduction to Modeling with Differential Equations
Overnight Homework 1
Due November 28, 2011, 8:00 am. Late submissions shall get 25% deduction of earned
scores.
Write your solutions in shortsize bond papers.
Determine whether the differential
Introduction to Modeling with Differential Equations
CHM 220

Fall 2012
Applications of First Order Differential Equations  (1.3)(2.7)(2.8)
1. Growth and Decay:
Consider the initial value problem:
dP ! kP, P!0" ! P 0 .
dt
Function P!t" represents population at the time t. When k " 0, the population is increasing and when
k #
Introduction to Modeling with Differential Equations
CHM 220

Fall 2012
Department of Chemical Engineering
University of San Carlos
Nasipit, Talamban, Cebu City, Philippines
SYLLABUS
Course No.
Descriptive Title
Credit Units
Prerequisites
:
:
:
:
Term
Teacher
:
:
CHM 220
Introduction to Modeling w/ Differential Equations
3
P
Introduction to Modeling with Differential Equations
CHM 220

Fall 2012
EQUATIONS REDUCIBLE TO VARIABLES SEPARABLE
1. HOMOGENEOUS EQUATIONS
A function f ( x , y ) is called homogeneous of degree n if f x, y n f x, y .
Example:
a. The function f x, y x 4 x 3 y is homogeneous with n 4 because
4
3
f x, y x x y 4 x 4 x 3 y 4f x,
Introduction to Modeling with Differential Equations
CHM 220

Fall 2012
32  rstOrder Equations for which Exact Solutions are Obtainable.
(b) (x'zy2 + Ixy")dx + N(x,.v)dy = 0. .
11. .Consider the differential equation _
(4x + 3y2)dx + nydy = 0.
(a) Show that this equation is not exact. _ . _
(b) Find an integrating factor
Introduction to Modeling with Differential Equations
CHM 220

Fall 2012
Differential Equations
Mathematics
By George L. EKOL
African Virtual university
Universit Virtuelle Africaine
Universidade Virtual Africana
African Virtual University
Notice
This document is published under the conditions of the Creative Commons
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Introduction to Modeling with Differential Equations
CHM 220

Fall 2012
Problem Set: Solving 1stOrder Ordinary Differential Equations
Solve the following differential equations or initialvalue problems (IVPs). Write your solutions in shortsize
(8.5x11) bond paper. Complete solution to this problem set is a requirement for