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 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. $y$] $\Rightarrow a \frac{d^{2}x}{dy^{2}}=0$ [Differentiating w.r.t. $y$] $\Rightarrow \frac{d^{2}x}{dy^{2}}=0\,\left[\because a \ne0\right]$ Hence, the required differential equation is $\frac{d^{2}x}{dy^{2}}=0$.