Published by:
CGP EDU Academic Team
Published on: August 11, 2026
A solution of the differential equation 
= 
is (C is an arbitrary constant) -
A
x 2 (cos y 2 – sin y 2 – 2C 
) = 2
) = 2
B
y 2 (cos x 2 – (sin y 2 – 2C 
) = 2
) = 2
C
x 2 (cos y 2 – sin y 2 – 
) = 4
) = 4
D
None of these
Text Solution
Verified by ExpertsThe correct answer is:
A
The given differential equation can be written as
= xy [x 2 sin y 2 + 1] ⇒ 
– 
y = y sin y 2 . This equation is reducible to linear equation, so putting – 1/x 2 = u, the last equation can be written as 
+ 2uy = 2y sin y 2
The integrating factor of this equation is 
. So required solution is u 
= 
sin y 2 . 
dy + C
= 
e t dt + C (t = y 2 ) = (1/2) 
(sin y 2 – cos y 2 ) + C
⇒ 2u = (sin y 2 – cos y 2 ) + C 
⇒ 2 = x 2 [cos y 2 – sin y 2 – 2 C 
]
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