How do I solve the Dirac equation in Japanese?


In a famous book of Richard Feynman there is a story about him struggling with
the Japanese language when it comes to keigo.

Take a look at the excerpt from “Surely You're Joking, Mr. Feynman!“, part 5:

> I was learning Japanese mainly for technical things, so I decided to check
> if this same problem existed among the scientists.  
>  At the institute the next day, I said to the guys in the office, “How would
> I say in Japanese, ‘I solve the Dirac Equation’?”  
>  They said such­-and­-so.  
>  “OK. Now I want to say, ‘Would you solve the Dirac Equation?’ — how do I
> say that?“ “Well, you have to use a different word for ‘solve,’” they say.  
>  “Why?” I protested. “When _I_ solve it, I do the same damn thing as when
> you solve it!”  
>  “Well, yes, but it’s a different word­­ it’s more polite.”  
>  I gave up. I decided that wasn’t the language for me, and stopped learning
> Japanese.

What would be those Japanese phrases like? Is there a keigo version even for a
verb like “solve” that has a rather abstract meaning to me?

