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SolveAlways
SolveAlways[
eqns
,
vars
] gives the values of parameters that make the equations eqns valid for all values of the variables vars.
Equations are given in the form lhs
==
rhs.
Simultaneous equations can be combined either in a list or with &&.
A single variable or a list of variables can be specified.
Example: SolveAlways[a x + b == 0, x] .
SolveAlways works primarily with linear and polynomial equations.
SolveAlways produces relations between parameters that appear in eqns, but are not in the list of variables vars.
SolveAlways[
eqns
,
vars
] is equivalent to Solve[!Eliminate[!
eqns
,
vars
]].
See the Mathematica book: Section 3.4.10.
See also: Eliminate, Solve, Reduce, PolynomialReduce.
Further Examples
Here is a simple example.
In[1]:= 
Out[1]= 
This fails because it involves transcendentals.
In[2]:= 
SolveAlways::ifun: Inverse functions are being used by SolveAlways, so some solutions may not be found.
Out[2]= 
This is how to make it work.
In[3]:= 
Out[3]= 
We check the result.
In[4]:= 
Out[4]= 
In[5]:= 
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