Form the differential equation of the family of hyperbolas having foci on x-axis and centre at origin.

Explanation

The equation of family of hyperbolas whose foci are on `X`-axis and whose centre is at origin, is
`(x^(2))/(a^(2))-(y^(2))/(b^(2))=1`

Differentiate with respect to x,
`(2x)/(a^(2))-(2yy')/(b^(2))=0implies(yy')/(x)=(a^(2))/(b^(2))`
Again, differentiate with respect to `x`,
`(x(d)/(dx)(yy')-yy'*(d)/(dx)(x))/( x^(2))=0`
`(x[yy''+(y')^(2)]-yy'*1)/(x^(2))=0`
`implies xyy''+x(y')^(2)-yy'=0`
which is the required differential equation.