​ random equation

$T=\int_{0}^{T}dt=\int_{0}^{L}\frac{dt}{ds}ds=\int_{0}^{L}\frac{ds}{v}=\frac{1}{\sqrt{2g}}\int_{0}^{L}\frac{ds}{\sqrt{{y}_{1}-y}} =\frac{1}{\sqrt{2g}}\int_{{x}_{1}}^{{x}_{3}}\sqrt{\frac{1+{y'}^{2}}{y}}dx$