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Find the differential equation of the fa...

Find the differential equation of the family of circles with their centre at the origin.

Text Solution

Verified by Experts

The correct Answer is:
`x+y(dy)/(dx)=0`

Equation of family of such concentrate circles is given by `x^(2)+y^(2)=r^(2)`.
Differentiating w.r.t. x, we get
`2x+2y(dy)/(dx)=0`
or `x+y(dy)/(dx)=`0, which is required differential equation.
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