FIRST ORDER
DIFFERENTIAL EQUATION:
Walking you towards an excellent grade and beyond that, a
blistering career path
Second semester 100 level – First semester 300 level
[A guide]
,As an undergraduate student I was one of the many students that were challenged
having to figure out Mathematics beyond the classroom work as there were not much
insights as to the real application of mathematics in the day-to-day engagement of real-
time work i.e. real-life work; and I know someone might be having such challenge too;
we were eager but didn’t have much exposure beyond the solving of the mathematical
problem; so in this discuss, I have intentionally taken time to incorporate it, so that you
will not only know how to solve the problem as a mathematics but equally know where
the problem originated from i.e. was modeled from; and the considerations it is being
used to take care of in those area via the using of the solutions gotten from the solved
equations which are the mathematical model that had resulted from there.
We are not all on the same step when it comes to learning; some are at the first step
while some others may be at step 2 or step 3. One thing that is always important is that
everyone is carried along. So, this content is structured to accommodate you at any
level you may have been. Start from the beginning or you can equally skip the areas
you may already be familiar with and jump straight to other area you are not.
There is a content guide, as you will notice, to help make your experience transversing
the content a pleasant one.
Mathematics is supposed to bring an aura of good feeling, at hearing or having to face
it, not elicit fear or indifference oozing from a sense of difficulty; so we have
intentionally taken it up to break down the complex issues, and had excitedly done so,
to make it an easy ride for you. I task you on being patient enough to go through it
attentively. Happy ride.
, The Contents
1. Just consider this! --- How confident are you when faced with a differential
equation?
2. The Scope of Coverage
3. How differential equations came about; and the real-life areas they arise from
4. What makes an equation a differential equation: definition
5. The equations: How to determine or know the order and types of a differential
equation
a. Separable Equations [even though the focus here is the order and type,
which apart from knowing what they are, key players in determining the
right method, it is worthwhile that you equally know the area of physical
interest they majorly arise]
b. Exact Equations
c. Non-exact Equations
d. Linear differential Equations
e. Non-linear differential equations:
6. Getting the Solution of these equations by methods of practical importance; and
as well interpretation of the results in terms of a given problem
a. Mathematical interpretation
b. Physical interpretation
7. A very important question worthy of note: existence and uniqueness
a. Conclusion
Page 1 of 44
, 1. Just consider this! ---How confident are you when faced with a
differential equation?
Breaking down complex issues into very simple and easy-to-handle issue is one thing
I delight doing; and if there is one place that is often the begging issue it is
mathematics. Some people view it with disdain being that they consider it as a difficult
fellow. Always being mindful of this, I do intentionally approach it with every sense of
duty to dismantle this perceived barrier and remove that toga of difficulty from it; and
bring to the fore the beautiful bride that it actually is. Peradventure you are one of such
persons before now, I am urging you to relax and take this walk through differential
equations with me so that you see it for what it actually is --- a friendly fellow.
The target is that by the time we would have come to the end of this journey, you will
comfortably and confidently look differential equations straight in the face and be
dismantling it being that you would have known the differential equations by their
order and types. These two “order and types” are key in determining the suitable
method to solving a given differential equation. You would have also known how to get
the solutions of differential equations by methods of practical importance. You will
equally be able to interpret the results in terms of a given problem. You will not equally
be left out from the all-important applications and areas of application in real time.
And equally be able to answer a very important question: do differential equations
always have a solution? And much more.
2. The Scope of Coverage
Differential equations are a very broad branch in Mathematics. It has Linear
differential equations and non-linear differential equations. These are the two major
branches of differential equations in relation to practical applications i.e. with respect
Page 2 of 44
DIFFERENTIAL EQUATION:
Walking you towards an excellent grade and beyond that, a
blistering career path
Second semester 100 level – First semester 300 level
[A guide]
,As an undergraduate student I was one of the many students that were challenged
having to figure out Mathematics beyond the classroom work as there were not much
insights as to the real application of mathematics in the day-to-day engagement of real-
time work i.e. real-life work; and I know someone might be having such challenge too;
we were eager but didn’t have much exposure beyond the solving of the mathematical
problem; so in this discuss, I have intentionally taken time to incorporate it, so that you
will not only know how to solve the problem as a mathematics but equally know where
the problem originated from i.e. was modeled from; and the considerations it is being
used to take care of in those area via the using of the solutions gotten from the solved
equations which are the mathematical model that had resulted from there.
We are not all on the same step when it comes to learning; some are at the first step
while some others may be at step 2 or step 3. One thing that is always important is that
everyone is carried along. So, this content is structured to accommodate you at any
level you may have been. Start from the beginning or you can equally skip the areas
you may already be familiar with and jump straight to other area you are not.
There is a content guide, as you will notice, to help make your experience transversing
the content a pleasant one.
Mathematics is supposed to bring an aura of good feeling, at hearing or having to face
it, not elicit fear or indifference oozing from a sense of difficulty; so we have
intentionally taken it up to break down the complex issues, and had excitedly done so,
to make it an easy ride for you. I task you on being patient enough to go through it
attentively. Happy ride.
, The Contents
1. Just consider this! --- How confident are you when faced with a differential
equation?
2. The Scope of Coverage
3. How differential equations came about; and the real-life areas they arise from
4. What makes an equation a differential equation: definition
5. The equations: How to determine or know the order and types of a differential
equation
a. Separable Equations [even though the focus here is the order and type,
which apart from knowing what they are, key players in determining the
right method, it is worthwhile that you equally know the area of physical
interest they majorly arise]
b. Exact Equations
c. Non-exact Equations
d. Linear differential Equations
e. Non-linear differential equations:
6. Getting the Solution of these equations by methods of practical importance; and
as well interpretation of the results in terms of a given problem
a. Mathematical interpretation
b. Physical interpretation
7. A very important question worthy of note: existence and uniqueness
a. Conclusion
Page 1 of 44
, 1. Just consider this! ---How confident are you when faced with a
differential equation?
Breaking down complex issues into very simple and easy-to-handle issue is one thing
I delight doing; and if there is one place that is often the begging issue it is
mathematics. Some people view it with disdain being that they consider it as a difficult
fellow. Always being mindful of this, I do intentionally approach it with every sense of
duty to dismantle this perceived barrier and remove that toga of difficulty from it; and
bring to the fore the beautiful bride that it actually is. Peradventure you are one of such
persons before now, I am urging you to relax and take this walk through differential
equations with me so that you see it for what it actually is --- a friendly fellow.
The target is that by the time we would have come to the end of this journey, you will
comfortably and confidently look differential equations straight in the face and be
dismantling it being that you would have known the differential equations by their
order and types. These two “order and types” are key in determining the suitable
method to solving a given differential equation. You would have also known how to get
the solutions of differential equations by methods of practical importance. You will
equally be able to interpret the results in terms of a given problem. You will not equally
be left out from the all-important applications and areas of application in real time.
And equally be able to answer a very important question: do differential equations
always have a solution? And much more.
2. The Scope of Coverage
Differential equations are a very broad branch in Mathematics. It has Linear
differential equations and non-linear differential equations. These are the two major
branches of differential equations in relation to practical applications i.e. with respect
Page 2 of 44
