CHAPTER 1

Question 1

Application of De

Answer 1

Exponential growth (Population)
Exponential Reduction or Decay

Question 2

The ____ of a D.E. is the same as the order of the highest-ordered derivative in the equation.

Answer 2

order

Question 3

The _____ of a D.E. is the same as the power (or exponent) to which the derivative of the highest order in the equation is raised.

Answer 3

degree

Question 4

A D.E. may be ______ or ______ as to the type of derivatives or differential appearing on the equation.

Answer 4

ordinary/partial

Question 5

The ______ is the relation involving only the variables and arbitrary constants, free of any
derivatives of differential, and consistent with, or satisfying, the given D.E

Answer 5

solution to a D.E.

Question 6

The most general solutions of a D.E. of the nth order contains_________.

Answer 6

arbitrary constants

Question 7

An ________ involves function and its derivatives. It contains only one independent variable and one or more of its derivatives with respect to the variable

Answer 7

ordinary differential equation

Question 8

A differential equation containing partial derivatives of the dependent variable (one or more) with more than one independent variable.

Answer 8

Partial differential equation

Question 9

A differential equation of the form
𝒅𝒚/𝒅𝒙 + 𝑷𝒚 = 𝑸,
where P and Q are constants or functions of x only is called a ________ differential equation.

Answer 9

first order linear

Question 10

In a system of differential equations used to describe a time-dependent process, a ________ is a function that appears in the equations and is only a function of time, and not of any of the other variables.

Answer 10

forcing function

Question 11

A ____ differential equation does not combine y or any of its derivatives through multiplication.

Answer 11

linear

Question 12

_______ contains functions of one of the dependent variable on its derivatives such as:
Trigonometric functions, Exponential functions, Logarithmic functions

Answer 12

Non-linear ODE

Question 13

A linear differential equation is ______ if the forcing function g(x) is 0.

Answer 13

homogenous

Question 14

The graph of the solutions of a differential equation are called its )_______

Answer 14

integral curves

Question 15

A solution of an ordinary differential equation of order n that involves exactly n essential arbitrary constants called also complete solution, general integral

Answer 15

General Solution

Question 16

A solution of a partial differential equation that involves arbitrary functions.

Answer 16

General Solution

Question 17

A ______ of a differential equation is a solution obtained from the General Solution by assigning
specific values to the arbitrary constants

Answer 17

Particular Solution

Question 18

sets the initial condition of the problem, normally at zero value of the independent variable, to obtain the value of the arbitrary constant

Answer 18

Initial Value Ploblem

Question 19

The term _______ is used when the independent variable is the time and the condition given is at zero-time, t=0

Answer 19

initial condition

Question 20

The term ______ is used if the independent variable is anyone of the spatial coordinates x, y or z and the
conditions given are for known values of anyone of these coordinates

Answer 20

boundary

Question 21

In application, an _____ is a result of the magnitude (dependent) of the function observed at any given time (independent)

Answer 21

arbitrary constant

Question 22

The graph of a solution of a differential equation is a ________.

Answer 22

solution curve

Question 23

The number of derivatives of the produced differential equation should be ______ to the number of distinct
arbitrary constants to be eliminated

Answer 23

equal