Consider a family of curves
`f(x,y,c_1,c_2 , ...... c_n) = 0` ....................(i)
where `c_1, c_2, ...... , c_n` are `n` independent parameters.
Equation `(i)` is known as an `n` parameter family of curves e.g. `y = mx` is `1`-parameter family of straight
lines `x^2 + y^2 +ax+ by= 0` is a two-parameter family of circles.
If we differentiate equation `(i)` `n` times w.r.t `x`, we will get n more relations between `x, y, c_1 c_2, ...... c_n`
and derivates of `y` with respect to `x`. By eliminating `c_1, c_2, ...... , c_n` from these `n` relations and
equation `(i)`, we get a differential equation.
Clearly order of this differential equation will be `n`, i.e., equal to the number of independent parameters
in the family of curves.
Consider a family of curves
`f(x,y,c_1,c_2 , ...... c_n) = 0` ....................(i)
where `c_1, c_2, ...... , c_n` are `n` independent parameters.
Equation `(i)` is known as an `n` parameter family of curves e.g. `y = mx` is `1`-parameter family of straight
lines `x^2 + y^2 +ax+ by= 0` is a two-parameter family of circles.
If we differentiate equation `(i)` `n` times w.r.t `x`, we will get n more relations between `x, y, c_1 c_2, ...... c_n`
and derivates of `y` with respect to `x`. By eliminating `c_1, c_2, ...... , c_n` from these `n` relations and
equation `(i)`, we get a differential equation.
Clearly order of this differential equation will be `n`, i.e., equal to the number of independent parameters
in the family of curves.