Q. The differential equation $y\ \frac{dy}{dx} + x = c$ represents
A) A family of hyperbolas
B) A family of circles whose centres are on the $y$-axis
C) A family of parabolas
D) A family of circles whose centres are on the $x$-axis
Explanation
(d)
Given differential equation is
$ydy = (c - x)dx$
$\Rightarrow$ $\frac{y^{2}}{2} = cx - \frac{x^{2}}{2} + d$
$\Rightarrow$ $y^{2} + x^{2} - 2cx - 2d = 0$
Hence, it represents a family of circles whose centres are on the $x$-axis.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.