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

Question

Philoid · Accepted Answer

We know that the equation of the family of ellipses having foci on y – 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.