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dong19841007

银虫 (小有名气)

[求助] matlab 指数函数的求解 已有2人参与

各位大神, 本人想计算一函数:Ae^(-3x)-Be^(3x)+Ce^(-x)+De^(x)=0 中x的值,其中A B C D是已知常数,分别为:0.3868  0.6127  0.0346  0.0247,不胜感激!
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liuqh

铁杆木虫 (正式写手)

【答案】应助回帖

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感谢参与,应助指数 +1
dong19841007: 金币+15, ★有帮助 2015-11-27 14:59:20
两边同时乘以e^(-3x),再设y=e^(2x)得:
A-B*y^3+C*y+D*y^2=0
这是一个三次方程,可以得到解析解
2楼2015-11-27 12:36:21
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wurongjun

专家顾问 (职业作家)

【答案】应助回帖

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感谢参与,应助指数 +1
dong19841007: 金币+15, ★有帮助 2015-11-27 14:59:25
>> solve('0.3868*exp(-3*x)-0.6127*exp(3*x)+0.0346*exp(-x)+0.0247*exp(x)','x')

ans =

[ -.86916955192864803062253473465446e-1+2.0899090876028300027275824953505*i]
[ -.86916955192864803062253473465446e-1-1.0516835659869632357350608879291*i]
[ -.86916955192864803062253473465446e-1-2.0899090876028300027275824953505*i]
[ -.86916955192864803062253473465446e-1+1.0516835659869632357350608879291*i]
[ -.56149917690505204568753325861134e-1+3.1415926535897932384626433832795*i]
[                                     -.56149917690505204568753325861134e-1]

>> double(ans)

ans =

  -0.0869 + 2.0899i
  -0.0869 - 1.0517i
  -0.0869 - 2.0899i
  -0.0869 + 1.0517i
  -0.0561 + 3.1416i
  -0.0561
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3楼2015-11-27 14:30:24
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