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Solving ODEs by inspection is ludicrous

In my advanced mathematics course the first method demonstrated by the professor for solving ODEs is "solution by inspection" which is powered by "intuitive experience" and I haven't been able to get past this.

We're halfway through the semester and I can solve almost everything the professor throws at us, but every now and again there will be a question that seems impossible that nobody can figure out. When the prof finally shows us the answer written beside it will be "by inspection".

Can someone guide me to some resources to provide me with the tools necessary to actually solve the equation instead of memorisation. Maths has always been a logical process to me and I would hate to have to "throw in the towel" and rely on rote "learning" just to be able to pass this course.

submitted by /u/Brouhoff
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from math https://ift.tt/2HNxoZ6
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