Published by:
CGP EDU Academic Team
Published on: August 12, 2026
If y ′ = 
, then its solution is -
Text Solution
Verified by ExpertsThe correct answer is:
A
Given, 
This is a homogeneous equation
Put y = vx ⇒ 
= v + x 
Given equation becomes
v + x 
= 
⇒ x 
= 
– v
⇒ 
dv = 
On integrating both sides
dv = 
Put (1 + v) 2 = t ⇒ 2(1 + v) dv = dt
⇒ 
= 
⇒ – 
log (2 – t) = log x + log c
⇒ – 
log [2 – (1 + v) 2 ] = log xc
⇒ – 
log [–v 2 – 2v + 1] = log xc
⇒ log 
= log xc
⇒ x 2 c 2 (1 – 2v – v 2 ) = 1
⇒ x 2 c 2 
= 1 
⇒ 
= 1
⇒ y 2 + 2xy – x 2 = c
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