Question

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

• A. $ \frac{d^2y}{dx^2} = 0 $
• B. $ \frac{dy}{dx} = 0 $
• C. $ \frac{dx}{dy} = 0 $
• D. None of these

Answer 1

Answer: (A)

The general equation of non-vertical lines is
$a x+b y=1$
On differentiating w.r.t. $x$, we get
$a+b \frac{d y}{d x}=0$
Again differentiating w.r.t. $x$, we get
$\frac{b d^{2} y}{d x^{2}}=0$
$\Rightarrow \frac{d^{2} y}{d x^{2}}=0$