Final Concepts

Question 1

It is possible to transform the non-exact differential equation by a judicious multiplication which we call as

Answer 1

integrating factor

Question 2

An ________ is a solution to a certain partial differential equation

Answer 2

integrating factor

Question 3

Integrating factors are generally obtained by

Answer 3

inspection

Question 4

In a way, integrating factor can easily be obtained by using formulas. These formulas involve the

Answer 4

test of
exactness

Question 5

is a generalized case of the linear form

Answer 5

Bernoulli Equation

Question 6

contains a certain expression in terms of the independent variable which makes it distinct from the linear form.

Answer 6

Bernoulli

Question 7

The expression ______ in terms of the dependent variable, is what makes it distinct from the linear form

Answer 7

y^n

Question 8

If G(x, y) represents a given one-parameter family of curves and R(x, y) is another one-parameter
family of curves, such that every curve of G intersects every curve of R at a fixed angle $, then R(x, y) is
called the ________ of the given family of curves G(x, y)

Answer 8

isogonal trajectories

Question 9

Certain types of substances decompose at a rate proportional to its amount at any instant: a chemical
process known as

Answer 9

exponential decay

Question 10

A colony of bacteria may increase at a rate
which varies directly as its number at any time: a relative but opposite process known as

Answer 10

exponential growth

Question 11

states that the rate of change of the temperature of a cooling body is
proportional to the difference between the temperature of the body and the constant temperature of the
medium surrounding the body

Answer 11

Newton’s Law of Cooling

Question 12

Note that in such process, T is greater than Ts. Thus, T-Ts is

Answer 12

positive

Question 13

Note that the temperature of the object T changes exponentially from the initial temperature 𝑇𝑜 of the object to the

Answer 13

limiting
temperature 𝑇

Question 14

A ________ is one in which an inductance L, resistance R, and a capacitance C, are
connected in series with a source of electromotive force of E volts.

Answer 14

simple closed electric circuit

Question 15

The differential equation necessary to solve the various problems relative to this circuit is derived with the use of the laws of

Answer 15

Ohm and Kirchoff

Question 16

is a circuit parameter which opposes a change in the current I (amperes)

Answer 16

inductance L (Henries)

Question 17

is a circuit parameter which opposes a change in voltage

Answer 17

capacitance C (farads)

Question 18

is a circuit parameter which opposes the a change in the current I (amperes)

Answer 18

resistance R (ohms)

Question 19

Q is the electric charge measured in

Answer 19

Coulombs

Question 20

states that “the algebraic sum of all potential around a closed electric circuit is zero”.

Answer 20

first law of Kirchoff

Question 21

Two relative problems may be expected under this condition:

i. When the e.m.f. E is constant
ii. When the e.m.f. E is given as a function of the time, t

Answer 21

True

Question 22

is the rate of change of the electric charge Q

Answer 22

current I

Question 23

Once k is chosen positive, the minus sign is required in
Newton’s law to make 𝑑𝑇
𝑑𝑡 negative in a

Answer 23

cooling process