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My differential equations have been written as

eqns = {Subscript[x, 1]'[t] == \[Alpha]*Subscript[x, 1][t]*Subscript[x, 3][t] -
  \[Beta]*Subscript[x, 1][t]*Subscript[x, 2][t], 
Subscript[x, 2]'[t] == \[Gamma]*Subscript[x, 2][t] - \[Delta]*Subscript[x, 1][t]*Subscript[x, 2][t], 
Subscript[x, 3]'[t] == \[Epsilon]*Subscript[x, 1][t] - \[Lambda]*Subscript[x, 2][t],
Subscript[x, 1][0] == 147100 + 15000,
Subscript[x, 2][0] == 178000,
Subscript[x, 3][0] == 723586 + 554776};

sol = DSolve[eqns, {Subscript[x, 1], Subscript[x, 2], Subscript[x, 3]}, t]
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closed as off-topic by Louis, RunnyKine, MarcoB, Öskå, m_goldberg May 4 at 0:01

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "The question is out of scope for this site. The answer to this question requires either advice from Wolfram support or the services of a professional consultant." – Louis, RunnyKine, MarcoB, Öskå, m_goldberg
If this question can be reworded to fit the rules in the help center, please edit the question.

Mathematica cannot solve this equation, so it returns the input. It is possible (likely) that this equation doesn't have a solution in terms of simple functions. Try NDSolve for a numerical solution. – Szabolcs Apr 14 '14 at 15:41

This is not an answer. I am just providing a version of the OPs code in an easier-to-read and easier-to-work-with form.

eqns = 
  {x1'[t] == α*x1[t]*x3[t] - β*x1[t]*x2[t], 
   x2'[t] == γ*x2[t] - δ*x1[t]*x2[t], 
   x3'[t] == ϵ*x1[t] - λ*x2[t], 
   x1[0] == 147100 + 15000, 
   x2[0] == 178000, 
   x3[0] == 723586 + 554776};

sol = DSolve[eqns, {x1, x2, x3}, t]
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