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Solve coupled equations in the steady state

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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