level 9
liyajx
楼主
{DSolve[{t''[s] - (xx'[s] t'[s])/(9000 (1 - xx[s]/9000)) == 0,
xx''[s] + xx'[s]^2/(
18000 (1 - xx[s]/9000)) + ((1 - xx[s]/9000) t'[s]^2)/18000 == 0,
t[0] == 0, t'[0] == 1, xx[0] == 0, xx'[0] == 0}, {t[s], xx[s]}, {s,
0, 1}],
DSolve[{t''[s] - (hh'[s] t'[s])/(9000 (1 - hh[s]/9000)) == 0,
hh''[s] + hh'[s]^2/(
18000 (1 - hh[s]/9000)) + ((1 - hh[s]/9000) t'[s]^2)/18000 == 0,
t[0] == 0, t'[0] == 1, hh[0] == 0, hh'[0] == 0}, {t[s], hh[s]}, {s,
0, 1}]}
(* Out: {{{t[s] -> 18000 ArcTan[s/18000], xx[s] -> -(s^2/36000)}}, {}} *)

2025年08月01日 08点08分
1
xx''[s] + xx'[s]^2/(
18000 (1 - xx[s]/9000)) + ((1 - xx[s]/9000) t'[s]^2)/18000 == 0,
t[0] == 0, t'[0] == 1, xx[0] == 0, xx'[0] == 0}, {t[s], xx[s]}, {s,
0, 1}],
DSolve[{t''[s] - (hh'[s] t'[s])/(9000 (1 - hh[s]/9000)) == 0,
hh''[s] + hh'[s]^2/(
18000 (1 - hh[s]/9000)) + ((1 - hh[s]/9000) t'[s]^2)/18000 == 0,
t[0] == 0, t'[0] == 1, hh[0] == 0, hh'[0] == 0}, {t[s], hh[s]}, {s,
0, 1}]}
(* Out: {{{t[s] -> 18000 ArcTan[s/18000], xx[s] -> -(s^2/36000)}}, {}} *)
