By the degree of a differential equation, when it is a polynomial equation in
derivatives, we mean the highest power (positive integral index) of the highest order
derivative involved in the given differential equation In view of the above definition, one may observe that differential equations (6), (7),
(8) and (9) each are of degree one, equation (10) is of degree two while the degree of
differential equation (11) is not defined �Note   Order and degree (if defined) of a differential equation are always
positive integers © NCERT
not to be republished
MATHEMATICS
382
Example 1 Find the order and degree, if defined, of each of the following differential
equations:
(i)
cos
0
dy
x
dx −
=
(ii)  
2
2
2
0
d y
dy
dy
xy
x
y
dx
dx
dx
⎛
⎞
+
−
=
⎜
⎟
⎝
⎠
(iii)
2
0
y
y
y
e ′
′′′ +
+
=
Solution
(i)
The highest order derivative present in the differential equation is dy
dx , so its
order is one