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Question: Answered & Verified by Expert
Which one of the following is the differential equation to family of circles having centre at the origin? $\quad$
MathematicsDifferential EquationsNDANDA 2010 (Phase 2)
Options:
  • A $\left(x^{2}-y^{2}\right) \frac{d y}{d x}=2 x y$
  • B $\left(x^{2}+y^{2}\right) \frac{d y}{d x}=2 x y$
  • C $\frac{d y}{d x}=\left(x^{2}+y^{2}\right)$
  • D $x d x+y d y=0$
Solution:
1417 Upvotes Verified Answer
The correct answer is: $x d x+y d y=0$
The equation of family of circles having centres at the origin is $x^{2}+y^{2}=r^{2}$
where $r^{\prime}$ is the radius. Differentiate both side w.r.t. $x$, we get
$$
2 x+2 y \frac{d y}{d x}=0
$$
$$
\begin{aligned}
& 2 x d x+2 y d y=0 \\
\Rightarrow \quad & x d x+y d y=0
\end{aligned}
$$
which is required differential equation.

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