MathGroup Archive: August 2004 [00340]

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can this be solved in Mathematica 5.0?
To: mathgroup at smc.vnet.net
Subject: [mg50140] can this be solved in Mathematica 5.0?
From: "Anonym2004" <anonym at bamboo.com>
Date: Tue, 17 Aug 2004 05:01:18 -0400 (EDT)
Sender: owner-wri-mathgroup at wolfram.com
Can the following equation:

Out[3]=
\!\({P\_1 == \(A\_4 + \[ExponentialE]\^\(\(-K\)\ T\_1\)\ C\_4 + B\_4\ \
T\_1\)\/\((\(-b\) + V\_1)\)\^5 + \(A\_3 + \[ExponentialE]\^\(\(-K\)\ T\_1\)\
\
C\_3 + B\_3\ T\_1\)\/\((\(-b\) + V\_1)\)\^4 + \(A\_2 + \
\[ExponentialE]\^\(\(-K\)\ T\_1\)\ C\_2 + B\_2\ T\_1\)\/\((\(-b\) + \
V\_1)\)\^3 + \(A\_1 + \[ExponentialE]\^\(\(-K\)\ T\_1\)\ C\_1 + B\_1\ \
T\_1\)\/\((\(-b\) + V\_1)\)\^2 + \(X\ T\_1\)\/\(\(-b\) + V\_1\),
P\_2 == \(A\_4 + \[ExponentialE]\^\(\(-K\)\ T\_2\)\ C\_4 + B\_4\ T\_2\)\/\
\((\(-b\) + V\_2)\)\^5 + \(A\_3 + \[ExponentialE]\^\(\(-K\)\ T\_2\)\ C\_3 +
B\
\_3\ T\_2\)\/\((\(-b\) + V\_2)\)\^4 + \(A\_2 + \[ExponentialE]\^\(\(-K\)\ \
T\_2\)\ C\_2 + B\_2\ T\_2\)\/\((\(-b\) + V\_2)\)\^3 + \(A\_1 + \
\[ExponentialE]\^\(\(-K\)\ T\_2\)\ C\_1 + B\_1\ T\_2\)\/\((\(-b\) + \
V\_2)\)\^2 + \(X\ T\_2\)\/\(\(-b\) + V\_2\),
P\_3 == \(A\_4 + \[ExponentialE]\^\(\(-K\)\ T\_3\)\ C\_4 + B\_4\ T\_3\)\/\
\((\(-b\) + V\_3)\)\^5 + \(A\_3 + \[ExponentialE]\^\(\(-K\)\ T\_3\)\ C\_3 +
B\
\_3\ T\_3\)\/\((\(-b\) + V\_3)\)\^4 + \(A\_2 + \[ExponentialE]\^\(\(-K\)\ \
T\_3\)\ C\_2 + B\_2\ T\_3\)\/\((\(-b\) + V\_3)\)\^3 + \(A\_1 + \
\[ExponentialE]\^\(\(-K\)\ T\_3\)\ C\_1 + B\_1\ T\_3\)\/\((\(-b\) + \
V\_3)\)\^2 + \(X\ T\_3\)\/\(\(-b\) + V\_3\),
P\_4 == \(A\_4 + \[ExponentialE]\^\(\(-K\)\ T\_4\)\ C\_4 + B\_4\ T\_4\)\/\
\((\(-b\) + V\_4)\)\^5 + \(A\_3 + \[ExponentialE]\^\(\(-K\)\ T\_4\)\ C\_3 +
B\
\_3\ T\_4\)\/\((\(-b\) + V\_4)\)\^4 + \(A\_2 + \[ExponentialE]\^\(\(-K\)\ \
T\_4\)\ C\_2 + B\_2\ T\_4\)\/\((\(-b\) + V\_4)\)\^3 + \(A\_1 + \
\[ExponentialE]\^\(\(-K\)\ T\_4\)\ C\_1 + B\_1\ T\_4\)\/\((\(-b\) + \
V\_4)\)\^2 + \(X\ T\_4\)\/\(\(-b\) + V\_4\),
P\_5 == \(A\_4 + \[ExponentialE]\^\(\(-K\)\ T\_5\)\ C\_4 + B\_4\ T\_5\)\/\
\((\(-b\) + V\_5)\)\^5 + \(A\_3 + \[ExponentialE]\^\(\(-K\)\ T\_5\)\ C\_3 +
B\
\_3\ T\_5\)\/\((\(-b\) + V\_5)\)\^4 + \(A\_2 + \[ExponentialE]\^\(\(-K\)\ \
T\_5\)\ C\_2 + B\_2\ T\_5\)\/\((\(-b\) + V\_5)\)\^3 + \(A\_1 + \
\[ExponentialE]\^\(\(-K\)\ T\_5\)\ C\_1 + B\_1\ T\_5\)\/\((\(-b\) + \
V\_5)\)\^2 + \(X\ T\_5\)\/\(\(-b\) + V\_5\),
P\_6 == \(A\_4 + \[ExponentialE]\^\(\(-K\)\ T\_6\)\ C\_4 + B\_4\ T\_6\)\/\
\((\(-b\) + V\_6)\)\^5 + \(A\_3 + \[ExponentialE]\^\(\(-K\)\ T\_6\)\ C\_3 +
B\
\_3\ T\_6\)\/\((\(-b\) + V\_6)\)\^4 + \(A\_2 + \[ExponentialE]\^\(\(-K\)\ \
T\_6\)\ C\_2 + B\_2\ T\_6\)\/\((\(-b\) + V\_6)\)\^3 + \(A\_1 + \
\[ExponentialE]\^\(\(-K\)\ T\_6\)\ C\_1 + B\_1\ T\_6\)\/\((\(-b\) + \
V\_6)\)\^2 + \(X\ T\_6\)\/\(\(-b\) + V\_6\),
P\_7 == \(A\_4 + \[ExponentialE]\^\(\(-K\)\ T\_7\)\ C\_4 + B\_4\ T\_7\)\/\
\((\(-b\) + V\_7)\)\^5 + \(A\_3 + \[ExponentialE]\^\(\(-K\)\ T\_7\)\ C\_3 +
B\
\_3\ T\_7\)\/\((\(-b\) + V\_7)\)\^4 + \(A\_2 + \[ExponentialE]\^\(\(-K\)\ \
T\_7\)\ C\_2 + B\_2\ T\_7\)\/\((\(-b\) + V\_7)\)\^3 + \(A\_1 + \
\[ExponentialE]\^\(\(-K\)\ T\_7\)\ C\_1 + B\_1\ T\_7\)\/\((\(-b\) + \
V\_7)\)\^2 + \(X\ T\_7\)\/\(\(-b\) + V\_7\),
P\_8 == \(A\_4 + \[ExponentialE]\^\(\(-K\)\ T\_8\)\ C\_4 + B\_4\ T\_8\)\/\
\((\(-b\) + V\_8)\)\^5 + \(A\_3 + \[ExponentialE]\^\(\(-K\)\ T\_8\)\ C\_3 +
B\
\_3\ T\_8\)\/\((\(-b\) + V\_8)\)\^4 + \(A\_2 + \[ExponentialE]\^\(\(-K\)\ \
T\_8\)\ C\_2 + B\_2\ T\_8\)\/\((\(-b\) + V\_8)\)\^3 + \(A\_1 + \
\[ExponentialE]\^\(\(-K\)\ T\_8\)\ C\_1 + B\_1\ T\_8\)\/\((\(-b\) + \
V\_8)\)\^2 + \(X\ T\_8\)\/\(\(-b\) + V\_8\),
P\_9 == \(A\_4 + \[ExponentialE]\^\(\(-K\)\ T\_9\)\ C\_4 + B\_4\ T\_9\)\/\
\((\(-b\) + V\_9)\)\^5 + \(A\_3 + \[ExponentialE]\^\(\(-K\)\ T\_9\)\ C\_3 +
B\
\_3\ T\_9\)\/\((\(-b\) + V\_9)\)\^4 + \(A\_2 + \[ExponentialE]\^\(\(-K\)\ \
T\_9\)\ C\_2 + B\_2\ T\_9\)\/\((\(-b\) + V\_9)\)\^3 + \(A\_1 + \
\[ExponentialE]\^\(\(-K\)\ T\_9\)\ C\_1 + B\_1\ T\_9\)\/\((\(-b\) + \
V\_9)\)\^2 + \(X\ T\_9\)\/\(\(-b\) + V\_9\),
P\_10 == \(A\_4 + \[ExponentialE]\^\(\(-K\)\ T\_10\)\ C\_4 + B\_4\ \
T\_10\)\/\((\(-b\) + V\_10)\)\^5 + \(A\_3 + \[ExponentialE]\^\(\(-K\)\ \
T\_10\)\ C\_3 + B\_3\ T\_10\)\/\((\(-b\) + V\_10)\)\^4 + \(A\_2 + \
\[ExponentialE]\^\(\(-K\)\ T\_10\)\ C\_2 + B\_2\ T\_10\)\/\((\(-b\) + \
V\_10)\)\^3 + \(A\_1 + \[ExponentialE]\^\(\(-K\)\ T\_10\)\ C\_1 + B\_1\
T\_10\
\)\/\((\(-b\) + V\_10)\)\^2 + \(X\ T\_10\)\/\(\(-b\) + V\_10\),
P\_11 == \(A\_4 + \[ExponentialE]\^\(\(-K\)\ T\_11\)\ C\_4 + B\_4\ \
T\_11\)\/\((\(-b\) + V\_11)\)\^5 + \(A\_3 + \[ExponentialE]\^\(\(-K\)\ \
T\_11\)\ C\_3 + B\_3\ T\_11\)\/\((\(-b\) + V\_11)\)\^4 + \(A\_2 + \
\[ExponentialE]\^\(\(-K\)\ T\_11\)\ C\_2 + B\_2\ T\_11\)\/\((\(-b\) + \
V\_11)\)\^3 + \(A\_1 + \[ExponentialE]\^\(\(-K\)\ T\_11\)\ C\_1 + B\_1\
T\_11\
\)\/\((\(-b\) + V\_11)\)\^2 + \(X\ T\_11\)\/\(\(-b\) + V\_11\),
P\_12 == \(A\_4 + \[ExponentialE]\^\(\(-K\)\ T\_12\)\ C\_4 + B\_4\ \
T\_12\)\/\((\(-b\) + V\_12)\)\^5 + \(A\_3 + \[ExponentialE]\^\(\(-K\)\ \
T\_12\)\ C\_3 + B\_3\ T\_12\)\/\((\(-b\) + V\_12)\)\^4 + \(A\_2 + \
\[ExponentialE]\^\(\(-K\)\ T\_12\)\ C\_2 + B\_2\ T\_12\)\/\((\(-b\) + \
V\_12)\)\^3 + \(A\_1 + \[ExponentialE]\^\(\(-K\)\ T\_12\)\ C\_1 + B\_1\
T\_12\
\)\/\((\(-b\) + V\_12)\)\^2 + \(X\ T\_12\)\/\(\(-b\) + V\_12\),
P\_13 == \(A\_4 + \[ExponentialE]\^\(\(-K\)\ T\_13\)\ C\_4 + B\_4\ \
T\_13\)\/\((\(-b\) + V\_13)\)\^5 + \(A\_3 + \[ExponentialE]\^\(\(-K\)\ \
T\_13\)\ C\_3 + B\_3\ T\_13\)\/\((\(-b\) + V\_13)\)\^4 + \(A\_2 + \
\[ExponentialE]\^\(\(-K\)\ T\_13\)\ C\_2 + B\_2\ T\_13\)\/\((\(-b\) + \
V\_13)\)\^3 + \(A\_1 + \[ExponentialE]\^\(\(-K\)\ T\_13\)\ C\_1 + B\_1\
T\_13\
\)\/\((\(-b\) + V\_13)\)\^2 + \(X\ T\_13\)\/\(\(-b\) + V\_13\),
P\_14 == \(A\_4 + \[ExponentialE]\^\(\(-K\)\ T\_14\)\ C\_4 + B\_4\ \
T\_14\)\/\((\(-b\) + V\_14)\)\^5 + \(A\_3 + \[ExponentialE]\^\(\(-K\)\ \
T\_14\)\ C\_3 + B\_3\ T\_14\)\/\((\(-b\) + V\_14)\)\^4 + \(A\_2 + \
\[ExponentialE]\^\(\(-K\)\ T\_14\)\ C\_2 + B\_2\ T\_14\)\/\((\(-b\) + \
V\_14)\)\^3 + \(A\_1 + \[ExponentialE]\^\(\(-K\)\ T\_14\)\ C\_1 + B\_1\
T\_14\
\)\/\((\(-b\) + V\_14)\)\^2 + \(X\ T\_14\)\/\(\(-b\) + V\_14\),
P\_15 == \(A\_4 + \[ExponentialE]\^\(\(-K\)\ T\_15\)\ C\_4 + B\_4\ \
T\_15\)\/\((\(-b\) + V\_15)\)\^5 + \(A\_3 + \[ExponentialE]\^\(\(-K\)\ \
T\_15\)\ C\_3 + B\_3\ T\_15\)\/\((\(-b\) + V\_15)\)\^4 + \(A\_2 + \
\[ExponentialE]\^\(\(-K\)\ T\_15\)\ C\_2 + B\_2\ T\_15\)\/\((\(-b\) + \
V\_15)\)\^3 + \(A\_1 + \[ExponentialE]\^\(\(-K\)\ T\_15\)\ C\_1 + B\_1\
T\_15\
\)\/\((\(-b\) + V\_15)\)\^2 + \(X\ T\_15\)\/\(\(-b\) + V\_15\)}\)

be solved for the following unknowns:

In[4]:=
\!\({X, b, K, A\_1, A\_2, A\_3, A\_4, B\_1, B\_2, B\_3, B\_4, C\_1, C\_2,
C\_3, C\_4}\)
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