Question

The differential equation of all non-vertical 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: (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. $x$]
$\Rightarrow b \frac{d^{2}\,y}{dx^{2}}=0$ [Differentiating w.r.t. $x$]
$\Rightarrow \frac{d^{2}\,y}{dx^{2}}=0\,\left[\because b \ne0\right]$
Hence, the required differential equation is $\frac{d^{2}\,y}{dx^{2}}=0$.