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

Answer: (B)

The general equation of all non-horizontal lines in a plane is $ax+by=1$, where $a\ne 0$.
Now, $ax+by=1$
$\Rightarrow a\frac{dx}{dy}+b=0$ [Differentiating w.r.t. $y$]
$\Rightarrow a\frac{d^{2}x}{d{y}^2}=0$ [Differentiating w.r.t. $y$]
$\Rightarrow \frac{d^{2}x}{d{y}^2}=0\left[\because a\ne 0\right]$
Hence, the required differential equation is $\frac{d^{2}x}{d{y}^2}=0$.