SolveAlways

Q: How can I solve the equation

[Graphics:inoutagr4.gif][Graphics:inoutagr14.gif]

for the variables a, [Graphics:inoutagr15.gif], and [Graphics:inoutagr16.gif]? [Graphics:inoutagr17.gif] does not give the answer I am looking for.

[Graphics:inoutagr4.gif][Graphics:inoutagr18.gif]
[Graphics:inoutagr4.gif][Graphics:inoutagr19.gif]
[Graphics:inoutagr4.gif][Graphics:inoutagr20.gif]

Daniel Lichtblau (danl@wolfram.com) answers: [Graphics:inoutagr21.gif] gives the values of parameters that make the equation valid for all values of the variables [Graphics:inoutagr22.gif] and [Graphics:inoutagr23.gif].

[Graphics:inoutagr4.gif][Graphics:inoutagr24.gif]
[Graphics:inoutagr4.gif][Graphics:inoutagr25.gif]

Another possibility is to use (implicit) series expansion.

[Graphics:inoutagr4.gif][Graphics:inoutagr26.gif]
[Graphics:inoutagr4.gif][Graphics:inoutagr27.gif]