If m and n are respectively the order and degree of the differential equation of the family of parabolas with focus at the origin and X -axis as its axis, then m n-m+n=

Step-by-step solution

The equation of the family of parabolas with focus at the origin and X -axis as its axis is given by array rlrl y^2 & =4 a(x+a)=4 a x+4 a^2 & & 2 y d y d x & =4 a & & a & = 1 2 y d y d x array aligned & 2 y d y d x =4 a & a= 1 2 y d y d x aligned From Eqs. (i) and (ii), we have y^2=2 x y d y d x +y^2 ( d y d x )^2 order =m=1 and degree =n=2 m n-m+n=1 2-1+2=3 .