设y'=p, 有:
pdp / dy= e^2y , pdp = e^(2y) dy
1/2 p² =1/2 e^(2y) +1/2 c₁,
代入y'(0) =0 即p(0)=0,得c₁=▬1
p= ±✔(e^2y-1) = dy/dχ,
dy
▬▬▬▬▬ 〓 ± dx
✔e^2y-1)
令e^y〓 sect ,y=lnsect,
dx= (sect tant)/ sect, 分子为tant,
积为 arcsec (e^y ) = ±x +c₂
代入条件,有 arcsec eº 〓 c₂ =0
所以有:arcsec (e^y)= ± x , e^y= ± secx
y= ln│secx│