Q. 23.6( 56 Votes )
In each of the question, form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.
y2 = a(b2 – x2)
Answer :
The given equation is y2 = a(b2 – x2)
Now, differentiating both sides w.r.t x, we get,
⇒ 2yy’ = -2ax
⇒ yy’ = -ax -------(1)
Now, again differentiating both sides, we get,
y’.y’ +yy’’ = -a
⇒ (y’)2 + yy” = -a --------(2)
Now, dividing equation (2) by (1), we get,
⇒ xyy” + x(y’)2 – yy” = 0
Therefore, the required differential equation is xyy” + x(y’)2 – yy” = 0.
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