Question

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

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

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.,
$2x+2y\frac{dy}{dx}=0$
$x+y\frac{dy}{dx}=\mathrm{0........}$(ii)
which represents the family of concentric circles given by Eq. (i). Then, Eq. (i) is a general solution of Eq. (ii).