Form Differential Equation By Eliminating And B In Ax2 By2 1

Form the differential equation by eliminating A and B in Ax2 – By2 = 1.

Answers:

We have equation of family of curves Ax2 – By2 = 1
On differentiating both sides w.r.t.x, we get
2Ax – 2Byy’ = 0
or Ax = Byy’  (i) 
Differentiating again both sides w.r.t.x, we get 
A = Byy” + By’²
From Eqs.(i) and (ii), we get 
(Byy” + By’²)x = Byy’
⇒ (yy” + y’²)x = yy’
⇒ xyy” + x(y”)² – yy’ = 0