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I'm trying to solve the ODE $\frac{\partial M}{\partial \tau} = [ 4 c_3 N(\tau) + c_1 ] M(\tau),$ where $N(\tau) = \frac{q}{2 c_3} \frac{ 1 }{c_2 e^{2 q \tau} + 1} - \left ( \frac{ q + c_1}{4 c_3} \right )$ for some parameters $\{c_1 , c_2 , c_3 , q \}$ that I would like to evaluate later.

I've set up the problem as follows

$Assumptions = 
Element[q, Reals] && q > 0 &&
Element[c3, Reals] && c3 > 0 &&
Element[const, Reals] &&
Element[c1, Reals];

Neqn[tau_] := (q/(2*c3))*(1/(const*Exp[2 * q*tau] + 1)) - (c1 + q)/(4*c3);
eqn = {y'[tau] == (4*c3*Neqn[tau] + c1)*y[tau] , y[0] == 0};
sol = DSolve[eqn, y[tau], tau] 

which is giving

{{y[tau] -> 0}}
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  • 2
    $\begingroup$ It might have to do with your initial condition; try omitting it and see how you like the solution. $\endgroup$ – b.gates.you.know.what Jan 4 '14 at 17:14
  • $\begingroup$ Hmm. You're correct. And I don't like the solution. Thanks! $\endgroup$ – Luap Nalehw Jan 4 '14 at 17:39

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