# Solving for variables that satisfy an equation

I have the following

p[c1_, c2_, w_] := Exp[(-2*ω/(σ^2))*(c2^2 + ω^2*c1^2)]*
Exp[(-1/(2*Σ))*(w - α*c2 - β*c1)^2]

SolveAlways[-D[c2*p[c1, c2, w], c1] +
D[((2*ω)*c2 + ((ω)^2)*c1)*p[c1, c2, w], c2] +
(1/2)*(σ^2)*D[p[c1, c2, w], {c2, 2}] -
D[(c2*(1 - 2*Sqrt[3]) - c1*(Sqrt[3]*ω))*p[c1, c2, w], w] +
(3/2)*((σ/ω)^2)*D[p[c1, c2, w], {w, 2}] == 0, {c1, c2, w, σ, ω}]

I am trying to solve for any α, β, Σ (in terms of c1, c2, w, σ, ω) that satisfies the previous equation. However, nothing results.

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From from the documentation of SolveAlways, "SolveAlways works primarily with linear and polynomial equations." – m_goldberg Jun 19 '14 at 1:49
@m_goldberg I see...maybe that's why I didn't get anything...thanks for that..I tried using Solve and it returned huge expressions for some of my unknowns, however, it wasn't able to solve all of them..can you kindly advise of any other alternatives? thanks! – Stoc Jun 19 '14 at 1:57
also...the answers were in terms of the other variables I wanted to solve for so this does not help me...I want to get α, β, Σ explicitly in terms of c1, c2, w, σ, ω – Stoc Jun 19 '14 at 2:00
Some responses to this post might help. Any but mine, that is. – Daniel Lichtblau Jun 19 '14 at 15:22