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    $\begingroup$ If you change initial condition k[t /; t <= 2 tau] == 0 to k[t /; t <= 0] == 0 it seems to work. $\endgroup$ Commented Jun 13, 2018 at 15:58
  • $\begingroup$ Thanks for the suggestion but I would like to keep it that way. Also how can i change the initial value for $x$ to $x(0)=0.02$? $\endgroup$ Commented Jun 13, 2018 at 18:34
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    $\begingroup$ If you use k[t /; t <= 0] == HeavisideTheta[t - 2 tau] you get a solution, but all values of y,y,k are zero. If you apply Reduce[{eqs, t == -1}] there seem to occur condtradictions. $\endgroup$ Commented Jun 14, 2018 at 7:01