1. Y.SARATH BABU
A.SHAMEER AHMED
PRESENTED BY:

2. Contents
Definatio
n
Types
Propertie
s and

3. DIFFERENTIAL EQUATIONS APPLICATIONS IN SCIENCE & ENGINEERING
Definition
These are the equations obtained eliminating of arbitrary
constants from f(x,y,z,a,b)=0 equation in which a,b are
constants.
A differential equation is an equation involving
derivatives of an unknown function and possibly
the function itself as well as the independent
variable.
Example
4 2 2 3
sin , ' 2 0, 0y x y y xy x y y x
1st order equations 2nd order equation

4. Differential equations was
invented by LEIBNITZ
It was developed by
JOHANN BERNOULLI

5.  The order of the differential equation is order of
the highest derivative in the differential equation.
Differential Equation ORDER
32x
dx
dy
0932
2
y
dx
dy
dx
yd
36
4
3
3
y
dx
dy
dx
yd
1
2
3

6. Differential Equation
Degree
032
2
ay
dx
dy
dx
yd
36
4
3
3
y
dx
dy
dx
yd
03
53
2
2
dx
dy
dx
yd
1
1
3
The degree of a differential equation is power of
the highest order derivative term in the differential
equation.

7. Derivatives These Are Two
Types
1. An ordinary differential equations
2. A partial differential equations
032
2
ay
dx
dy
dx
yd
32x
dx
dy
02
2
2
2
y
u
x
u
04
4
4
4
t
u
x
u
1
1
2
2

8. Newton’s law of
cooling
sTT
dt
dT
Ex: A murder victim is discovered and a lieutenant was to estimate the time of
death. The body is loacted in a room that body kept at a constant temperture of
68◦F . The lieutenant arrived at 9.30P.M and measured the body temperture as
94.4◦F at that time. Another measurement of the body temperture at 11P.M is
89.2◦F
Ans : time of death 53.8 minutes
Rate Of Decay Of
Radioactive Materials
y is the quantity present at any
time(t)
dy
y
dt
─

9. Newton's Second Law In Dynamics
Law of natural
growth or decay N(t) is amount of substance at
‘t’

10. In Schrodinger
Wave Equation
The Schrodinger equation is the name of the basic non-
relativistic wave equation used in one version of
quantum mechanics to describe the behaviour of a
particle in a field of force. There is the time dependant
equation used for describing progressive
waves, applicable to the motion of free particles. And
the time independent form of this equation used for
describing standing waves.

11. In Laplace transforms
RL circuit
L di/dt + Ri =
E

12. Heat Equation In
Thermo Dynamics
Example:

13. 10
1. Free falling stone
g
dt
sd
2
2
2. Spring vertical displacement
ky
dt
yd
m 2
2
where y is displacement,
m is mass and
k is spring constant
a=-g

14. Jacobian
Properties
•If the Jacobian(J) value is zero
then the given two relations are
dependent.
•If the Jacobian(J) value is not
zero then the given two relations
are independent.