Book: Mathematics Part-II
Chapter: 9. Differential Equations
Subject: Maths - Class 12th
Q. No. 9 of Exercise 9.3
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9
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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