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When I search meaning, both 原因 and 要因 mean cause.

解析 and 分析 mean analysis.

But I think there will be little different meaning.

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  • There's also 起因 which is similar to 原因 and used (mostly?) in writing, but it has a different usage pattern in terms of particles. Commented Jun 14, 2016 at 5:32
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    I suggest you break this question in two: one for the difference between 要因、原因(、起因) and another one with 解析、分析(、解剖). Commented Jun 14, 2016 at 5:42

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From my personal experience,

「原因」 is like a general cause, perhaps one of many.

「原因は結果の反対語である」 - "The cause is the opposite of the result"

「要因」 is the primary cause.

「他の原因はたくさんあったのですが、飲酒運転が要因だったようです。」 
  - "Though there were many other factors, drunk driving seems to have been the primary cause"

「解析」 is a word for the process of developing a logical theory about how something works or how or why something happened by analyzing the information already available, like when you analyze statistics.

「経済を解析するプロジェクト」 - "a project to analyze the economy"

「分析」 is a general word for breaking something up and analyzing its parts to get more information about it, like you might analyze a meteorite.

「事故の原因はまだ分析しなければなりません」 
  - "(We) still need to analyze the causes of the accident"
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