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NDA 2013
Exam
NDA
Year
2013
Subject
Mathematics
Chapter
Differential Equations

NDA 2013 · Mathematics · Differential Equations

The differential equation of all circles whose centres are at the...

The differential equation of all circles whose centres are at the origin is

Options

  1. Adydx=yx\frac{d y}{d x}=\frac{y}{x}
  2. Bdydx=xy\frac{d y}{d x}=\frac{x}{y}
  3. Cdydx=−xy\frac{d y}{d x}=-\frac{x}{y}
  4. DNone of the above

Correct answer

C. dydx=−xy\frac{d y}{d x}=-\frac{x}{y}

Step-by-step solution

Standard equation of circle where centre is at the origin is x2+y2=r2x^2+y^2=r^2 Differentiating both sides w.r.t. xx, we get 2x+2y⋅dydx=0 or, dydx=−xy\begin{aligned} 2 x+2 y \cdot \frac{d y}{d x} & =0 \\ \text{ or, } \frac{d y}{d x} & =-\frac{x}{y} \end{aligned}
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