this is an euler lagrange equation problem from the book- "classical mechanics-John R. Taylor", problem-6.11 find the path function for which ∫ √x*√(1+y'^2) dx is stationary. the answer is- x= C+(y-D)^2/4C, the equation of a parabola. here the euler lagrange equation will work on f=√x*√(1+y'^2). since ∂f/∂y= 0, so ∂f/∂y'= const → √x*y'/ √(1+y'^2)= constant. then i dont get how i get from here to the equation of the parabola. any help?