Published by:
CGP EDU Academic Team
Published on: August 13, 2026
The curves satisfying the differential equation (1 – x 2 ) y ′ + xy = ax are -
Text Solution
Verified by ExpertsThe correct answer is:
A
The given equation is linear in y and can be written as
+ 
y = 
Its integrating factor is
= 
= 
if –1 < x < 1
and if x 2 > 1 then I.F. = 
= 
= – 
a 
⇒ y 
= 
+ C
⇒ y = a + C 
⇒ (y – a) 2 = C 2 (1 – x 2 ) ⇒ (y – a) 2 + C 2 x 2 = C 2
Thus if – 1 < x < 1 the given equation represents an ellipse. If x 2 > 1 then the solution is of the form – (y – a) 2 – C 2 x 2 = C 2 which represents a hyperbola
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