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

Family of all circles in the x y -planewith radius 5 units with center (x₁, y₁ ) is (x-x₁ )^2+ (y-y₁ )^2=5^2 (x-x₁ )=- (y-y₁ ) y^ Now Eq. (ii) diff again w.r.t ' x ', we get aligned 2+2 (y^ (y-y₁ )+ (y^ )^2 ] & =0 (y-y₁ ) & = 1- (y^ )^2 y^ aligned Sub. values in Eq. (i) aligned = [ 1+ (y^ )^2 y^ y^ ^2+ [ 1+ (y^ )^2 y^ ] & =25 (1+y^ 2 ) (y^ )^2 (y^ )^2+ 1+ (y^ )^2 (y^ )^2 & =25 (1+y^ )^3 (y^ )^2 & =25 25 (y^ )^2= [1+ (y^ )^2 ]^3 & aligned So, order =2 and degree =2 aligned & l=2 and m=2 & Now, 2 l+3 m=2 2+3 2 & =4+6