Question

Find the differential equation of all non-horizontal lines in a plane.

Answer 1

Equation of line is $ax+by=\mathrm{1....}\left(1\right),$,$a\ne 0$

diff (1) w.r.t $y$

$a.\frac{dx}{dy}+b=0$ (1) w.r.t $y$

$a\frac{d^{2}x}{d{y}^2}=0$

$\Rightarrow$ $\frac{d^{2}x}{d{y}^2}=0$

$\therefore$ differential equation of all non-horizontal lines is

$\frac{d^{2}x}{d{y}^2}=0$

Now diff