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Totally guessing but I think the specific ODE course might be a little harder since it is already a big topic without matrices and then you add in LA (so a littler tougher than just a classical ODE course).

That said, I would do the ODE course first. It is much more fundamental than contour integration is to engineering. Almost everything is a diffyQ in engineering. Use of complex variables is actually rather rare in normal engineering homework.

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