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enter image description hereenter image description here

I do not know how to handle the integro-term.

ieqn = 1 - 6.25*10^5*x[t] + 1.234*10^4*Integrate[x'[u]/Sqrt[t - u], {u, 0, t}] == 1.5924*x''[t]; ic = {x[0] == 0, x'[0] == 0}; sol = DSolve[{ieqn, ic}, x[t], t]; Plot[x[t] /. sol, {t, 0, 0.007}]

enter image description here enter image description here

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    $\begingroup$ Is this about Wolfram Mathematica? Have you tried do find something in integro-differential topics? $\endgroup$ Commented Jul 3, 2018 at 12:39
  • $\begingroup$ the value of t do not change the output of the figure or curve,and i do not know what's wrong with my code $\endgroup$ Commented Jul 4, 2018 at 1:26
  • $\begingroup$ Which version are you in? In v11.2 DSolve returns unevaluated. $\endgroup$ Commented Jul 5, 2018 at 10:38

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I use "11.3.0 for Microsoft Windows (64-bit) (March 7, 2018)".

Copy-pasting the proposed code I receive only a slew of errors and no output (only the axes, but no graph).

Instead, writing:

f[u_?NumericQ] := x'[u]/Sqrt[t - u] ieqn = 1 - 6.25 10^5 x[t] + 1.2341 10^4 Integrate[f[u], {u, 0, t}] == 1.5924 x''[t]; ic = {x[0] == 0, x'[0] == 0}; xsol = NDSolveValue[{ieqn, ic}, x, {t, 0, 0.01}] // Quiet; Plot[xsol[t], {t, 0, 0.01}] // Quiet

I get:

enter image description here

where the two Quiet still hide a series of errors.

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  • $\begingroup$ I'm afraid this solution is not reliable, because you've hidden the x'[u] in a blackbox function, NDSolve won't be able to handle it corectly. $\endgroup$ Commented Jul 5, 2018 at 10:26

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