Both mean to "check out". Analyzing is about dismantling, separating things into their constituent elements and to find out the cause of something; what makes it tick; why it works etc. Investigate is inquring into or to follow up of something. In such questions like "what's the difference between A and B". Just type that into Google and look up the answers for yourself.

As far as I know, if you have a car, analyzing would imply to separate the different pieces of the car and find out what are they made of. On the other hand, to investigate would be examining how the pieces go together. So, analyzing would be the "what" (the object)and investigating would be the "how" (the process). Sometimes they are synonyms.

They mean the same thing but are used differently. In both cases you will be seeking to get information.