Question

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

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

Answer 1

Answer: (B)

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

Answer 2

The general equation of all non-horizontal lines in

xy–plane is $ax + by = 1$, where a$\neq 0.$

$\Rightarrow a\frac{dx}{dy} + b = 0$ [Diff. w.r.to y]

$\Rightarrow a\frac{d^{2}x}{dy^{2}} = 0$ [Diff. w.r.to y]

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

Hence, the required differential equations is $\frac{d^{2}x}{dy^{2}} = 0$