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The phrase "a unique solution of" is correct and usable in written English.
It can be used in contexts such as mathematics, problem-solving, or discussions about specific answers to questions or equations.
Example: "In this case, we have determined that there is a unique solution of the equation that satisfies all given conditions."
Alternatives: "a singular answer to" or "one distinct solution for".
Exact(60)
Then there is a unique solution of (1.2) with (1.8).
Then there exists a unique solution of problem (1.11), (2.1).
Hence, there exists a unique solution of (3.5) on J. □.
where is a unique solution of the variational inequality (3.4).
Obviously, is a unique solution of the problem (3.1).
Consequently, there exists a unique solution of equation (19).
That is, is a unique solution of (2.14).
This gives a unique solution of (1.2) for which (3.44).
Hence, there exists a unique solution of (1.1).
Hence, u is a unique solution of (32 - 33 32 - 33
From Lemma 3.2, there exists a unique solution of (3.19).
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com