Question

The differential equation of all non-horizontal lines in a plane is _____

• A. $\frac{d^{2}y}{d{x}^2}=0$
• B. $\frac{d^{2}x}{d{y}^2}=0$
• C. $\frac{dy}{dx}=0$
• D. $\frac{dx}{dy}=0$

Answer 1

The correct option is A $\frac{d^{2}y}{d{x}^2}=0$

Equation of non horizontal line in a plane is $y=mx+c$

Where $m$ is the slope

$\Rightarrow y=mx+c$

Since there are two arbitrary constants we shall differentiate two times

Differentiate w.r.t $x$

$\Rightarrow \frac{dy}{dx}=m$

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