If l and m are order and degree of a differential equation of all the straight lines at constant distance of P units from the origin, then l m 2 + l 2 m =

Step-by-step solution

Any straight lines at constant distance of P units from the origin is given by x cos α + y sin α = P Differentiating both the sides w.r.t. x , we get cos α + d y d x sin α = 0 i.e. d y d x = - cot α ⇒ cos α = - d y d x 1 + d y d x 2 ,   sin α = 1 1 + d y d x 2 x - d y d x 1 + d y d x 2 + y 1 1 + d y d x 2 = P ⇒ - x d y d x + y = P 1 + d y d x 2 Squaring both sides, we get x 2 d y d x 2 - 2 x y d y d x + y 2 = P 2 1 + d y d x 2 Hence, order of the differential equa