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Previously, I ask an NDSolve questions(https://mathematica.stackexchange.com/questions/84885/how-to-solve-the-differential-equation-with-duhamels-integral), but now a more sophisticated one:

NDSolve[{0.01-10 (0.01 t-x[t]) + (3 Integrate[(1+10 (0.01 (t-τ)-x[t-τ])) x'[t-τ]/Sqrt[τ], {τ, 0, t}])/10^7 == 10 x''[t], 
x[0] == 0, x'[0] == 0}, x, {t, 0, 10}]

How to solve it?

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    $\begingroup$ Why not help Mathematica out a bit and see if you can turn your integro-differential equation into an ODE? $\endgroup$ Jun 18 '15 at 10:31
  • $\begingroup$ @Guess who it is Thanks for your good advise. Maybe I should ask this question in Mathematics. $\endgroup$
    – Scott Wang
    Jun 18 '15 at 15:12
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    $\begingroup$ @ScottWang That is not what guesswho was hinting at. The suggestion is to take the derivative of your main equation to get rid of the integral and make it a real ordinary differential equation. $\endgroup$ Jun 19 '15 at 7:46
  • $\begingroup$ @Sjoerd C. de Vries I have asked this in Math. This question will be closed. Sorry for bothering. $\endgroup$
    – Scott Wang
    Jun 19 '15 at 8:16
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    $\begingroup$ I'm sorry, but this is much more difficult than your original problem and beyond my reach now. BTW, do you create this equation based on some reference or just in a… casual way? $\endgroup$
    – xzczd
    Jun 19 '15 at 11:57

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