Question

The differential equation satisfied by all the straight lines $xy$- plane (not parallel to $y$-axis) is:

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

Answer 1

Answer: (B)

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

Any equation of line in $xy$ plane is given by, $y=mx+c$

where $m$ and $c$ are parameters

Now differentiate the line,

$\Rightarrow \frac{dy}{dx}=m$

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