       solving eq.

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

```Hi!

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:= f[x]*a + f[x]*x==g[x]
Out= a f[x] + x f[x] == g[x]
In:= Solve[%,f[x]]
g[x]
Out= {{f[x] -> -----}}
a + x
In:=

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

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

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

Out= 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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