Q. The differential equation of the family of lines whose slope is equal to $y$-intercept, is
A) $(x + 1)\ \frac{dy}{dx} - y = 0\ \$
B) $(x + 1)\ \frac{dy}{dx} + y = 0$
C) $\frac{dy}{dx} = \frac{x - 1}{y - 1}$
D) $\frac{dy}{dx} = \frac{x + 1}{y + 1}$
Explanation
(a)
Equation of line whose slope is equal to y intercept, is
$y = cx + c = c(x + 1)$
$\Rightarrow$ $\frac{dy}{dx} = c$
$\therefore$ $\frac{dy}{dx} = \frac{y}{x + 1}$
$\Rightarrow$ $(x + 1)\frac{dy}{dx} - y = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.