Q. Form of the differential equation of all family of lines $y = mx + \frac{4}{m}$ by eliminating the arbitrary constant $m$ is
A) $\frac{d^{2}y}{dx^{2}} = 0$
B) $x\left( \frac{dy}{dx} \right)^{2} - y\frac{dy}{dx} + 4 = 0$
C) $x\left( \frac{dy}{dx} \right)^{2} + y\frac{dy}{dx} + 4 = 0$
D) $\frac{dy}{dx} = 0$
Explanation
(b)
$y = mx + \frac{4}{m}$ …(i)
$\therefore$ $\frac{dy}{dx} = m$
From Eq. (i), we get
$y = x\left( \frac{dy}{dx} \right) + \frac{4}{\left( \frac{dy}{dx} \right)}$
$\Rightarrow$ $y\left( \frac{dy}{dx} \right)^{\ } = x\ \left( \frac{dy}{dx} \right)^{2} + 4$
$\Rightarrow$ $x\left( \frac{dy}{dx} \right)^{2} - y\ \frac{dy}{dx} + 4 = 0$
Which is required differential equations.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.