�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 It is a polynomial equation in y′ and the highest power raised to dy
dx
is one, so its degree is one (ii)
The highest order derivative present in the given differential equation is 
2
d y2
dx
, so
its order is two