Explicit solutions are obtained in the limit of a small E-field.
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The canonical form may be viewed as an explicit solution of the linear system.
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:There rarely is an explicit solution.
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However, Hamilton's equations usually don't reduce the difficulty of finding explicit solutions.
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While explicit solutions can be found for equations that are quintic and higher degree equations, such as
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A closed-form or analytic solution is sometimes referred to as an "'explicit solution " '.
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For example, the following explicit solution using the atan2 ( y, x ) function will be valid for-\ pi:
8.
Even the answers to real questions began with vague hints, so a player could choose to stop short of getting explicit solutions to the puzzles.
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Besides their practical use in the evaluation of integrals and the explicit solution of certain differential equations, they have deep connections with elliptic curves and modular forms.
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One way of finding such explicit solutions is to reduce the equations to equations of lower dimension, preferably ordinary differential equations, which can often be solved exactly.
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