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)

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$.