Order of differential equation is the order of highest order derivative in differential equation.

1. Differential
Equation
Prof. Suvarna Bhagwat
Assistant Professor
Department of Applied Sciences & Engineering
Hope Foundation’s
International Institute of Information Technology, I²IT

2. ORDER & DEGREE
ORDER OF DIFFERENTIAL
EQUATION
Definition:
Order of differential equation
is the order of highest order
derivative in differential
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Tel - +91 20 22933441 / 2 / 3 | Website - www.isquareit.edu.in ; Email - info@isquareit.edu.in

3. Example:
Order of highest order
derivative =2
Order of differential
equation=2
Hope Foundation’s International Institute of Information Technology, I²IT, P-14 Rajiv Gandhi Infotech Park, Hinjawadi, Pune - 411
057
Tel - +91 20 22933441 / 2 / 3 | Website - www.isquareit.edu.in ; Email - info@isquareit.edu.in
02
2
 y
dx
yd

4. DEGREE OF DIFFERENTIAL
EQUATION
Definition:
The degree of differential equation is
the degree of highest order derivative
free from radicals and fractions.
Hope Foundation’s International Institute of Information Technology, I²IT, P-14 Rajiv Gandhi Infotech Park, Hinjawadi, Pune - 411 057
Tel - +91 20 22933441 / 2 / 3 | Website - www.isquareit.edu.in ; Email - info@isquareit.edu.in

5. Example:
Degree of highest order
derivative =1
Degree of differential
equation=1Hope Foundation’s International Institute of Information Technology, I²IT, P-14 Rajiv Gandhi Infotech Park, Hinjawadi, Pune - 411 057
Tel - +91 20 22933441 / 2 / 3 | Website - www.isquareit.edu.in ; Email - info@isquareit.edu.in
02
2
 y
dx
yd

6. Exercise:
Find the order & degree of differential
equation
Hope Foundation’s International Institute of Information Technology, I²IT, P-14 Rajiv Gandhi Infotech Park, Hinjawadi, Pune - 411 057
Tel - +91 20 22933441 / 2 / 3 | Website - www.isquareit.edu.in ; Email - info@isquareit.edu.in
2
2
23
2
22
2
2
2
3.4
01.3
.2
1
32
.1























dx
yd
y
dx
dy
dx
yd
dx
dy
ny
dx
dy
x
dx
yd
x
yx
yx
dx
dy

7. FORMATION OF DIFFERENTIAL
EQUATION FROM GENERAL
SOLUTION
1. If general solution contains ‘n’ no. of
constants then differentiate equation
‘n’
no. of times.
(No.of differentiation = No.of arbitraray
constants)
2.Elliminate the arbitrary constants.
Hope Foundation’s International Institute of Information Technology, I²IT, P-14 Rajiv Gandhi Infotech Park, Hinjawadi, Pune - 411 057
Tel - +91 20 22933441 / 2 / 3 | Website - www.isquareit.edu.in ; Email - info@isquareit.edu.in

8. Example
 Form the differential equation whose
general solution is
Sol.
Given
Hope Foundation’s International Institute of Information Technology, I²IT, P-14 Rajiv Gandhi Infotech Park, Hinjawadi, Pune - 411 057
Tel - +91 20 22933441 / 2 / 3 | Website - www.isquareit.edu.in ; Email - info@isquareit.edu.in
.32 xx
ebeay 
1.n32
eqebeay xx


9. Hope Foundation’s International Institute of Information Technology, I²IT, P-14 Rajiv Gandhi Infotech Park, Hinjawadi, Pune - 411 057
Tel - +91 20 22933441 / 2 / 3 | Website - www.isquareit.edu.in ; Email - info@isquareit.edu.in
equationaldifferentirequired065y
constantsarbitraryngelliminati1,2,3equationUsing
3.94
w.r.toatingdifferentiAgain
2.32y
havewe,w.r.t.atingDifferenti
2constantarbitraryNo.of
12
n32
2
n32
1








yy
eqbeaey
x
eqbeae
x
xx
xx

10. For details, please contact
Suvarna Bhagwat
suvarnab@isquareit.edu.in
Department of Applied Sciences & Engineering
Hope Foundation’s
International Institute of Information Technology, I²IT
P-14,Rajiv Gandhi Infotech Park
MIDC Phase 1, Hinjawadi, Pune – 411057
Tel - +91 20 22933441/2/3
www.isquareit.edu.in | info@isquareit.edu.in