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x=a-b*(exp((c*x+y)/(e*f))-1)-(c*x+y)/d¡£³ýxºÍy£¬ÆäËûµÄ¶¼Êdz£Á¿£¬Ïë°ÑxÓ÷ûºÅ±íʾ³öÀ´¡£ÊÂʵÉÏxºÍyµÄ¹ØÏµÍ¼Èçͼ£º×ÝÖáΪx£¬ºáÖáΪy¡£

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> In solve at 83

ans =

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Èç¹û°Ñ·½³ÌºóÃæÐ¡²¿·ÖÈ¥µô£¬¼ò»¯Îª£º¡®x-a+b*(exp((c*x+y)/(e*f))-1¡¯£¬µ¹ÊÇÄܵõ½½á¹û£ºans =

a + b - (e*f*lambertw(0, (b*c*exp(y/(e*f))*exp((c*(a + b))/(e*f)))/(e*f)))/c¡£
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jerkwin

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csgt0: ½ð±Ò+1, лл 2013-04-22 17:57:30
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x+b*exp(a*x) = c
È»ºóÀûÓÃLambert W function¾Í¿ÉÒÔ°Ñx±íʾ³öÀ´ÁË

» ±¾ÌûÒÑ»ñµÃµÄºì»¨£¨×îÐÂ10¶ä£©

2Â¥2013-04-21 22:34:18
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lhf530001541

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2Â¥: Originally posted by jerkwin at 2013-04-21 22:34:18
Äã°ÑËü»¯¼òһϣ¬Äܵõ½ÈçÏÂÐÎʽµÄxµÄ·½³Ì£º
x+b*exp(a*x) = c
È»ºóÀûÓÃLambert W function¾Í¿ÉÒÔ°Ñx±íʾ³öÀ´ÁË

лл¹þ£¬ÎÒÊÔ¹ýÁË£¬»¹ÊDz»ÐС£
ÓÃsolve>>x+b*exp(a*x)-cµÃ²»µ½½á¹û£¬
¸Ä³Ésolve('x-exp(c*x+d)/a+b/a',x)£¬Ò²¾ÍÊÇ"a*x+b=exp(c*x+d)"
µÃµ½ÁË:- lambertw(0, -(c*exp(d))/(a*exp((b*c)/a)))/c - b/a
°ÑÎҵĹ«Ê½¸Ä³É"a*x+b=exp(c*x+d)"ÐÎʽºó£¬µÃµ½£º
x=-(a*d+b*d-y)/(c+d)-e*f/c*lambertw(0,-c*c*b*d/(e*f*(c+d))*exp((d*y+c*a*d+c*b*d)/(e*f*(c+d)))/(e*f)+(a*d+b*d-y)*c/((e*f)*(c+d)));
¿ÉÊÇ´úÈëÊý×Ö£ºy=0:1:40;
a=3.5;
b=0.0000000001;
c=3.5;
d=700;
e=66;
f=0.0257;
µÃµ½µÄxÊÇÐéÊý£¬ÕâÊÇÔõô»ØÊÂѽ£¿lambertw(0,   )²»Ó¦¸Ã¶¼ÊÇʵÊýÂð£¿
3Â¥2013-04-22 15:53:14
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jerkwin

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csgt0: ½ð±Ò+1, лл 2013-04-25 15:54:38
lhf530001541: ½ð±Ò+10, ¡ïÓаïÖú, лл°ïÖú¹þ£¬Õâ¸öÐв»Í¨£¬»¹ÊǵÃÏë±ðµÄ°ì·¨~ 2013-04-26 09:40:21
È¥¶Á¶ÁLambert W functionµÄÐÔÖÊ£¬Äã¾ÍÖªµÀÁË¡£Lambert W(x)µÄ¶¨ÒåÓòΪ[1/e, inf]£¬²»ÊÇÄãËæ±ãÊÔÊÔ¾ÍÄܶԵġ£
4Â¥2013-04-22 19:57:27
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