What is the difference between the two sentences?
Write the equation of the following data?
Write the equation for the following data?

Is there any significant difference between these two prepositions
here? Please help.

It's an equation for the data (for the purpose of describing the data) --

not an equation of the data. That would be an equation belonging to the data. What would that mean???
"The equation for immortality": the equation which prescribes how to attain immortality
"The equation of immortality": the equation which is proper to immortality, which can mean the above, or the equation to which you become familiar/know when reaching immortality, and perhaps other meanings
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CJ, how would you translate an Anatoliy Dneprov's book's title — "The equation of (for) immortality". I'd go for "of"...
 Marius Hancu's reply was promoted to an answer.
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Ant_222CJ, how would you translate an Anatoliy Dneprov's book's title — "The equation of (for) immortality". I'd go for "of"...
I don't advise translating a title until you've translated the whole book. Emotion: smile In other words, a translator might have to know the contents of the book to decide which shade of meaning would be best to express that title in a foreign language. I assume you are familiar with the book and findof better than for. I'm willing to trust your judgment on this point. Emotion: smile
Thank you, CJ and Marius. Sure I know whereof I speak Emotion: wink The formula does belong to immortality in the sence H2O belongs to water, so "of" is better. Many thanks.