UPSC NDA Math Model Paper 8

Given equation is
y2=a(b2−x2)
Differentiating w.r.t x
⇒ 2yy' = a(-2x)
⇒ yy' = -ax ...(i)
Differentiating w.r.t x again
⇒ yy'' + (y')2 = -a ...(ii)
From (i) and (ii) we get
⇒yy′=x(yy′′+(y′)2)
⇒yy′−xyy′′−x(y′)2=0