Among the options given below, from which option a differential equation of order two can be formed?
Among the options given below, from which option a differential equation of order two can be formed?
All circles passing through origin
All parabolas passing through origin and having focus on x -axis
All the lines passing through the origin
All hyperbolas of the form $\mathrm{x}^2-\mathrm{y}^2=\mathrm{k}^2$
Solution
Equation of circles passing through origin
$x^2+y^2+2 g x+2 f y=0$
where $g$ and $f$ are constants
So, 2 arbitrary constants
$\Rightarrow$ Order of differential equation will be 2 .