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I don't know why is not working?!!

Clear["Global`*"]
x[t] = x0 Exp[y0 (t - 1)]; 
t0 = 1; \Xi = 0.3; \Gamma = 1.33; \Lambda = 0.7; 
eqns = {y0^2 - (k*(1 - 2/(3*\Gamma)))/Exp[y0*(t - t0)] - (\Xi/\Gamma)*y0 - \Lambda}; 
f[t_] := y0^2 - (k*(1 - 2/(3*\Gamma)))/Exp[y0*(t - t0)] - (\Xi/\Gamma)*y0 - \Lambda; 
Solve[eqns == 0, y0]
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  • $\begingroup$ Have you tried using Solve with all of your assumptions entered? $\endgroup$ Jan 11 at 15:29
  • $\begingroup$ Recommend you write eqns = {y[x]^2 - a*y[x]*Sqrt[y[x]^2 + b*x[t]^-2 - f] + b*x[t]^-2 - a*f ==0} /. y[x] -> x'[t]/x[t]; Otherwise if you run the line more than once, you'll get strange things happening. $\endgroup$
    – MikeY
    Jan 11 at 15:34
  • $\begingroup$ okay, thanks for your hint. $\endgroup$ Jan 11 at 15:47
  • $\begingroup$ CA Trevillian, you mean " Solve [ {eqns , x[1] == 1} , y , t ]" $\endgroup$ Jan 11 at 15:57
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    $\begingroup$ You are wrong. "x'[t] / x[t] == Constant" implies an exponential, not a power law. $\endgroup$ Jan 11 at 16:41