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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? $\endgroup$ Commented Jun 18, 2015 at 10:31
  • $\begingroup$ @Guess who it is Thanks for your good advise. Maybe I should ask this question in Mathematics. $\endgroup$ Commented Jun 18, 2015 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. $\endgroup$ Commented Jun 19, 2015 at 7:46
  • $\begingroup$ @Sjoerd C. de Vries I have asked this in Math. This question will be closed. Sorry for bothering. $\endgroup$ Commented Jun 19, 2015 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? $\endgroup$ Commented Jun 19, 2015 at 11:57

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