Form the differential equation of family of lines situated at a constant distance `p` from the origin.

Explanation

All such lnes are tangent to circle of radius p.
Equation of tangent to circle `x^(2)+y^(2)=p^(2)`, having slope m is `y=mx+psqrt(1+m^(2))`, where `m=(dy)/(dx)`
`therefore y=(dy)/(dx)+psqrt(1+((dy)/(dx))^(2)`
or `(y-x(dy)/(dx))^(2)=p^(2)(1+((dy)/(dx))^(2))`
Which is required differential equation.
Here, order is 1 and degree is 2.