Question

The differential equation of all non-vertical 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: (A)

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