"namely" vs. "in particular"

Solution 1:

I think both are bad.

According to my dictionary(Genius English-Japanese Grand Dictionary),

"Namely" is inserted for an explanation of something, more concrete than "that is to say".

And

"namely" is not used at the first place of a sentence.

For example:

the youngest girl,namely Mary.

Three students were mentioned,namely John, Sarah and Sylvia.

In your example, "namely" is used at the first place of a sentence.

"In particular" is the antonym of "in general".

When you have selections to do something, you chose one of them.

For example:

This particular book. (It is the only book that I can achieve my purpose.There are many books in the world)

"Do you have anything to do?" "Nothing in particular"

particular = particularis(latin language) particle + ar(means like in latin language)

The equation has a unique solution.

The sentence says "Only one solution" at the first time,clearly.

I think that "in particular" is not used in the next sentence, because there is no selection for solutions.

Your sentence will be good if you change the sentence like this.

The equation has a unique solution, namely, the straight line between A and B.

On the above reason, "in particular"

The equation has good solutions. In particular, it is the straight line between A and B.

If you use like the above, the first sentence is as well as the second sentence.