Mathematica Asked by mehrosadat ebrahimi on August 18, 2021
I want to solve 16 coupled differential equations in the steady state.
Among the answers, I only require two of the answers. But the Mathematica does not show me the answers in detail!!!
Can anybody please help me?
My code is as follows:
How can I get only the answer of v33 and v44 in details?
equil = {2 (-[Kappa] + [Lambda] Cos[[Phi]]) v11 + ([CapitalDelta]
+ [Lambda] Sin[[Phi]]) (v12 + v21) +
g (v14 + v41) + [Kappa]/
2 (1 + 2 [ScriptCapitalN] +
2 [ScriptCapitalM] Cos[[Theta]]), -2 [Kappa] v12 + (
[CapitalDelta] + [Lambda] Sin[[Phi]]) v22 + (-[CapitalDelta] +
[Lambda] Sin[[Phi]]) v11 +
g (v42 -
v13) + [Kappa] [ScriptCapitalM] Sin[[Theta]], (-[Kappa] -
[Gamma] + [Lambda] Cos[[Phi]]) v13 + ([CapitalDelta] + [Lambda]
Sin[[Phi]]) v23 +
g (v12 +
v43) + [Delta] v14, (-[Kappa] - [Gamma] + [Lambda] Cos[
[Phi]]) v14 + ([CapitalDelta] + [Lambda] Sin[[Phi]]) v24 +
g (v44 -
v11) - [Delta] v13, (-[CapitalDelta] + [Lambda]
Sin[[Phi]]) v11 + ([CapitalDelta] + [Lambda] Sin[[Phi]]) v22 -
2 [Kappa] v21 +
g (v24 -
v31) + [Kappa] [ScriptCapitalM] Sin[[Theta]], (-
[CapitalDelta] + [Lambda] Sin[[Phi]]) (v12 + v21) -
2 ([Kappa] + [Lambda] Cos[[Phi]]) v22 -
g (v23 + v32) + [Kappa]/
2 (1 + 2 [ScriptCapitalN] -
2 [ScriptCapitalM] Cos[[Theta]]), (-[CapitalDelta] +
[Lambda] Sin[[Phi]]) v13 + (-[Kappa] - [Gamma] - [Lambda] Cos[
[Phi]]) v23 +
g (v22 -
v33) + [Delta] v24, (-[Delta] + [Lambda] Sin[[Phi]]) v14 +
(-[Kappa] - [Gamma] - [Lambda] Cos[[Phi]]) v24 -
g (v34 + v21) - [Delta] v23,
(-[Kappa] - [Gamma] + [Lambda] Cos[[Phi]]) v31 + (
[CapitalDelta] + [Lambda] Sin[[Phi]]) v32 +
g (v21 +
v34) + [Delta] v41, (-[CapitalDelta] + [Lambda]
Sin[[Phi]]) v31 + (-[Kappa] - [Gamma] - [Lambda] Cos[[Phi]]) v32
+ g (v22 - v33) + [Delta] v42, -2 [Gamma] v33 +
g (v23 + v32) + [Delta] (v34 + v43) + [Gamma]/
2 (1 + 2 m), -2 [Gamma] v34 +
g (v24 - v31) + [Delta] (v44 -
v33), (-[Kappa] - [Gamma] + [Lambda] Cos[[Phi]]) v41 + (
[CapitalDelta] + [Lambda] Sin[[Phi]]) v42 +
g (v44 -
v11) - [Delta] v31, (-[CapitalDelta] + [Lambda]
Sin[[Phi]]) v41 + (-[Kappa] - [Gamma] - [Lambda] Cos[[Phi]]) v42
- g (v12 + v43) - [Delta] v32, -2 [Gamma] v43 +
g (v42 - v13) + [Delta] (v44 - v33), -2 [Gamma] v44 -
g (v14 + v41) - [Delta] (v34 + v43) + [Gamma]/2 (1 + 2 m)};
Solve[equil == 0, {v11, v12, v13, v14, v21, v22, v23, v24, v31, v32,
v33, v34, v41, v42, v43, v44}]
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