If m and n are 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

Equation of family of parabola with focus at origin and the X -axis its axis is aligned & & y^2 & =-4 a(x-a) & & y^2 & =-4 a x+4 a^2 & & 2 y y^ & =-4 a & & a & =- y y^ 2 aligned Putting the value of a in Eq. (i), we get aligned & y^2=2 y y^ (x+ y y^ 2 ) & y=2 y^ (2 x+y y^ ) 2 & y=2 x y^ +y y^ 2 & y ( d y d x )^2+2 x d y d x -y=0 aligned gathered m= order =1 n= degree =2 m n-m+n=2-1+2=3 gathered