Q. 74.0( 4 Votes )

Form the differential equation corresponding to y2 – 2 ay + x2 = a2 by eliminating a.

Answer :

y2 – 2 a y + x2 = a2


On differentiating, with respect to x we get,





Putting this value of a in the given equation, we get,






y2y'2 – 2y2y'2 – 2xyy' + x2y'2 = y2 y'2 + 2xyy' + x2


y2y'2 – 2y2y'2 – 2xyy' + x2y'2 – y2 y'2 – 2xyy' – x2 = 0


⇒ – 4xyy' + y'2x2 – x2 – 2y'2y2 = 0


y’2(x2 – 2y2) – 4xyy’ – x2 = 0


So, y’2(x2 – 2y2) – 4xyy’ – x2 = 0


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