If l and m are the degree and the order respectively of the differential equation of the family of all circles in the X Y plane with radius 5 units, then 2 l + 3 m =

Step-by-step solution

Let the coordinates of the centre of the circle be h , k and radius be r . Then, equation of circle is x - h 2 + y - k 2 = 5 2       . . 1 Differentiating both sides w.r.t. x , we get 2 x - h + 2 y - k y ' = 0 ⇒ x - h = - y - k y '     . . . i Again differentiating w.r.t. x , we get 1 = - y ' 2 + y - k y ' ' ⇒ y - k = - 1 + y ' 2 y ' '       . . . i i Now, equation i becomes ⇒ x - h = 1 + y ' 2 y ' ' y '     . . . i i i Substitu