This document provides an introduction and overview of differential equations including: - It defines differential equations as equations that relate an unknown function to its derivatives. - It classifies differential equations as ordinary or partial, and discusses homogeneous differential equations which can be solved using separation of variables. - It provides examples of linear differential equations and discusses their applications in areas like software development, modeling natural phenomena, and theories. - In conclusion, it states that differential equations are essential for both engineers and non-engineers as they underpin many software programs and describe the natural world.

1. Wellcome
to our
presentation

2. Prime university

3. Differential
Equation

6.  Ordinary & Partial
Differential Equation
 Introduction of
Differential Equation
 Homogeneous
Differential Equation
 Application of
Differential
Equation
 Linear
Differential Equation
CONTENTS
 Classification of
Differential Equation

7. Differential Equation
An equation wich involves unknown function of
one several that relates the value
of the function itself and its derivatives of various
orders

8. Classification of Differential Equation

9. Homogeneous Differential Equation
A first Differential Equation is Homogeneous when it can be in this
from
𝑑𝑦
𝑑𝑥
= F(
𝑦
𝑥
)
We can solve it using separation of variables but first we create a new
variable V =
𝑌
𝑋
v =
𝑌
𝑋
𝑖𝑠 𝑎𝑙𝑠𝑜 𝑢𝑠𝑒 𝑎𝑠 𝑦 = 𝑣𝑥
𝑑𝑦
𝑑𝑥
=
𝑑(𝑉𝑋)
𝑑𝑥
= 𝑉
𝑑𝑋
𝑑𝑥
+X
𝑑𝑉
𝑑𝑥
so we can solve Differential Equation
u 𝑠𝑖𝑛𝑔 𝑌 = 𝑉𝑋 𝑎𝑛𝑑
𝑑𝑦
𝑑𝑥
=V+X
𝑑𝑣
𝑑𝑥

10. Ordinary
differential
equation
Ode 𝑑2 𝑦
𝑑𝑥2+7
𝑑𝑦
𝑑𝑥
− 𝑦 = 10
Partial
differential
equation
Pde 𝜕 2
𝑦
𝜕𝑥2
+7
𝜕𝑦
𝜕𝑥
− 𝑦 = 10

11. Linear Differential Equation
A Differential Equation of the from – p,q always x or
constant function
𝑑𝑦
𝑑𝑥
+py =Q Where P and Q be the
functions of x or constant
Example :
𝑑2 𝑦
𝑑𝑥2 +3
𝑑𝑦
𝑑𝑥
+9y-0

12. Is there any side that Have The actuall use
of DIFFerential equation in real life????
Why we need to
learn differential
equ ?????

13.  Application of
Differential Equation
Creating softwares
Creating Games,
Aspects of Algorithms
Bots , Networking
Mother nature
Artificial
Intelligence
Theories &
Explanations

14. SOFTWARE’S
The use of differential Equations to underrstand
computer Hardware Belongs to Applied physics or
Electrical Engineering

15. MOTHER NATURE
Differential Equation is an
esential tool for describe the
nature of the physical univers

16. Conclusion
Finnally we can say differential equation is an essential
part for both Engineer and non –enginner .the things we
can see which is software based is made with
differential equation. New software r program daily .
And for that Differential Equation is Needed

18. Thank you All