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The phrase "the exact solution" is correct and can be used in written English.
For example, "The mathematician worked tirelessly to find the exact solution to the equation."
Exact(60)
The exact solution is u(r) = r2 cosh(r).
The exact solution is presented.
The exact solution is illustrated by specific examples.
The convergence of iterates to the exact solution is shown.
"But Benton says that in the end no one has the exact solution.
F.M., N.B. and W.C. obtained the exact solution for the steady-state density matrix.
Examples are given with comparison with the exact solution.
Such series are uniformly convergent to the exact solution.
with the exact solution.
which is the exact solution.
The exact solution of (4.14) for is.
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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