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May 27 at 19:26 comment added Sidharth Ghoshal a possibly unhelpful idea but my first guess. If the solutions of the ODE form a bounded structure (such as a nice-enough lie group) then it becomes possible to select a random point from the structure and therefore a random solution to the original ODE similar to a real variable taking on a random value from $[0,1]$ or a random point on the surface of a sphere. But if we are dealing with an unbounded structure that is no longer such a well defined concept (hence my qualifier of possibly unhelpful).
May 27 at 18:46 history edited Peter CC BY-SA 4.0
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May 27 at 18:44 history edited Peter CC BY-SA 4.0
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S May 27 at 18:44 review First questions
May 27 at 18:57
S May 27 at 18:44 history asked Peter CC BY-SA 4.0