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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 

{MPLTEXT 0 21 40 "This uses MAPLE to find the solution of " }}{PARA 0 

"" 0 "" {MPLTEXT 0 21 52 "              sqrt(r/(cr+1)) dr/dt = +/-(2GM

_e)^0.5 " }}{PARA 0 "" 0 "" {MPLTEXT 0 21 72 "using the initial substi

tution   u = cr+1.   Hence, we need to integrate" }}{PARA 0 "" 0 "" 

{MPLTEXT 0 21 58 "              sqrt((u-1)/u) du/dt = +/-(2GM_e)^0.5 c

^(1.5)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {MPLTEXT 0 

21 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "int(sqrt(u^2-u)/u

,u);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$-%%sqrtG6#,&*$)%\"uG\"\"#

\"\"\"F-F+!\"\"F-F-*&#F-F,F--%#lnG6#,(#F.F,F-F+F-F$F-F-F." }}}{EXCHG 

{PARA 0 "" 0 "" {MPLTEXT 0 21 18 "Hence, we obtain  " }}{PARA 0 "" 0 "

" {MPLTEXT 0 21 70 "            ((cr+1)^2-(cr+1))-ln(-1/2+(cr+1)+sqrt(

(cr+1)^2-(cr+1)))/2 " }}{PARA 0 "" 0 "" {MPLTEXT 0 21 56 "            \+

             = +/-(2GM_e)^0.5 c^(1.5) t + C " }}{PARA 0 "" 0 "" 

{MPLTEXT 0 21 2 "  " }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" 

{MPLTEXT 0 21 66 "We now want to solve this for  r(t). (This is perhap

s very messy.)" }}}}{MARK "3 0 0" 66 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 

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