There is an analytic solution to the discrete time equations.

Each analytic solution is infinite in space and/or time.

The moments of the logit-normal distribution have no analytic solution.

This system is non-linear, and does not admit a generic analytic solution.

However, analytic solutions are sometimes useful for certain applications, and many mathematicians have tried to develop them.

Analytic solutions typically are also simply an equation that can give a quick answer based on a few basic parameters.

Some special cases of third-body perturbations have approximate analytic solutions.

For simple tunneling-barrier models, such as the rectangular barrier, an analytic solution exists.

There are exact, analytic solution for certain values of , in particular: .

As an alternative to drawing the phasor diagram, an analytic solution is possible for and in terms of the measurements.

This restriction leads to a linear differential equation of motion, and a simple analytic solution.

This analytic solution is only possible when the primitive equations are linearized and simplified.

For decades, speech recognition seemed to hit an impasse as scientists sought descriptive and analytic solution.

The only known analytic solutions to the classical equations of motion are marginal deformations.

Generally, a two-dimensional integral over complex variables has to be solved and in many cases, an analytic solution is not available.

The analytic solution of the eigenvalues and eigenvectors in strong coupling regime is also given.

For arbitrary values of the force constant, k, the Schrödinger equation does not have an analytic solution.

A suite of 2D and 3D analytic solutions ("elements") are available for different governing equations.

The analytic solution of the optimal control often involves extensive approximations but can still produce useful algorithms.

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Existential problems don't have analytic solutions.

Due to the difficulty in finding analytic solutions to most problems of interest, computer modeling and simulation is typically used to analyze orbital motion.

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Computer simulation is often used as an adjunct to, or substitute for, modeling systems for which simple closed form analytic solutions are not possible.

Simulation models on the other hand, utilize numerical techniques to solve problems for which analytic solutions are impractical or impossible.