how would you know if there is a solution to the differential equation?
can you give an example of an equation you are talking?
some of the differential equations doesn't have a solution so how would we know if the soltuion really exists?
This is hard to answer without an example. there are many equations without a solution but to test would depend on the equation. If you wanted to check, try for things like that cannot mathematically work like dividing by 0. I hope this helps.
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