Question Number 164564 by Rahul_99 last updated on 18/Jan/22
$$ \\ $$$${when}\:{F}\:{does}\:{not}\:{contain}\:{y}\:{explicity}\:.\:{Find}\:{the}\:{extremals}\:{of} \\ $$$$\underset{{x}_{\mathrm{1}} } {\overset{{x}_{\mathrm{2}} } {\int}}\frac{{y}'^{\mathrm{2}} }{{x}^{\mathrm{2}} }{dx} \\ $$