# 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.

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