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I have two coupled integrodifferential equations, as shown in the image attached. coupled equations

I am trying to solve them using a Laplace transform, as follows

\[Alpha]cont[\[Tau]_] := (E^(I (\[Tau]) \[Omega]0) gab^2 \[Pi]^(3/2) r0^2 \[Rho]0)/(Sqrt[2] \[HBar]^2 (r0^2 + (I (\[Tau]) \[HBar])/mb)^(3/2))
\[Alpha]s = LaplaceTransform[\[Alpha]cont[\[Tau]], \[Tau], s];
sols1 = c1s /. Solve[s c1s - 1 == -\[Alpha]s (c1s + c2s), c1s]
sols2 = c2s /. Solve[s c2s - 0 == -\[Alpha]s (c1s + c2s), c2s]

so that I can then evaluate the functions using the Stehfest algorithm. However, I am unable to produce this.

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    $\begingroup$ What issue have you encountered exactly? Does the code return any errors? If so, which ones? If not, where does it stop working? $\endgroup$ – MarcoB Mar 16 at 13:03
  • $\begingroup$ If you probably mean ? :$$\text{c1}'(t)=-\int_0^t (\text{c1}(\tau )+\text{c2}(\tau )) \text{$\alpha $cont}(\tau ) \, d\tau$$ then LaplaceTransform in this case, nothing will do. $\endgroup$ – Mariusz Iwaniuk Mar 16 at 14:11

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