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


We know that the equation of the family of hyperbolas having foci on x – axis and the centre at origin is

-------(1)



Now, differentiating equation (1) w.r.t. x, we get,



--------(2)


Now, again differentiating w.r.t. x, we get,





Let us substitute the value in eq. (2), we get,



x(y’)2 + xyy” - yy’ = 0


xyy” + x(y’)2 – yy’ = 0


Therefore, the required differential equation is xyy” + x(y’)2 – yy’ = 0.


9
1