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solving eq.

  • To: mathgroup at (mathgroup notes)
  • Subject: solving eq.
  • From: Zdravko Balorda <zdravc at robo.fer.yu>
  • Date: Fri, 17 Jan 92 8:48:10 MET


Lately, I have been working with solving systems of
transcendental  equations and I found it quite
difficult as perhaps  one would expect it to be.
I wonder how can i help Mathematica in solving
such problems. I found it very difficult even to 
simply rearrange an equation, like to collect
together Sqrt[...] terms, Sin[x...] terms etc. Let me
give an example:

a*Sin[x] + b*Cos[x] == c

This equation has a simple solution if one transformes it
into quadratic algebraic form substituting sines and
cosines with S, Sqrt[1-S^2], respectively. 

On the other hand things like Collect[] works on polynomials
only. And what about moving things from one side of an
equation to another side.

The following works just fine:
In[1]:= f[x]*a + f[x]*x==g[x]
Out[1]= a f[x] + x f[x] == g[x]
In[2]:= Solve[%,f[x]]
Out[2]= {{f[x] -> -----}}
                  a + x

while adding 10 to both sides and then solving it
In[3]:= f[x]*a + f[x]*x==g[x]
Out[3]= a f[x] + x f[x] == g[x]

In[4]:= % + 10
Out[4]= 10 + (a f[x] + x f[x] == g[x])

In[5]:= Solve[%,f[x]]
Solve::eq: 10 + (a f[x] + x f[x] == g[x])
     is not an equation or system of equations.

Out[5]= Solve[10 + (a f[x] + x f[x] == g[x]), f[x]]

Are there any tricks known to more experienced Mathematica
users, or perhaps this is not really a problem at all?

Regards, Zdravko Balorda, zdravc at robo.fer.yu

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