Question

The differential equation which represents the family of concentric circles $x^2+y^2=r^2$ is given by

• A. $x-y \frac{d y}{d x}=0$
• B. $x+y \frac{d y}{d x}=0$
• C. $y-x \frac{d y}{d x}=0$
• D. $y+x \frac{d y}{d x}=0$

Answer 1

Answer: (B)

The equation of family of concentric circles is
$x^2+y^2=r^2 ....$(i)
The differential equation must be free from $r$ because $r$ is different for different members of the family. This equation is obtained by differentiating Eq. (i) w.r.t. x, i.e.,
$2 x+2 y \frac{d y}{d x}=0$
$x+y \frac{d y}{d x}=0 ........$(ii)
which represents the family of concentric circles given by Eq. (i). Then, Eq. (i) is a general solution of Eq. (ii).