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The phrase "obtain the solution" is correct and usable in written English.
It can be used in a variety of contexts where someone is trying to solve a problem. For example, "We need to obtain the solution to this problem as quickly as possible."
Exact(60)
And we give an algorithm to obtain the solution of the problem in the 'Solution of formulation' section.
Simulated annealing algorithm is used to obtain the solution.
Genetic algorithm is applied to obtain the solution of this model.
Ant colony optimization technique is used to obtain the solution of the design problem.
Then, a branch and bound algorithm embedded project scheduling is developed to obtain the solution.
Then differential quadrature method (DQM) is employed to obtain the solution.
Furthermore, different boundary conditions are applied to obtain the solution for different electrochemical systems.
The newly developed pb-2 Rayleigh-Ritz method is applied to obtain the solution.
To obtain the solution the shape function was approximated by Chebyshev series.
A numerical technique is employed to obtain the solution in the physical domain.
A numerical inversion technique has been applied to obtain the solution in the physical domain.
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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