Explicit solutions are obtained in the limit of a small E-field.
2.
The canonical form may be viewed as an explicit solution of the linear system.
3.
:There rarely is an explicit solution.
4.
However, Hamilton's equations usually don't reduce the difficulty of finding explicit solutions.
5.
While explicit solutions can be found for equations that are quintic and higher degree equations, such as
6.
A closed-form or analytic solution is sometimes referred to as an "'explicit solution " '.
7.
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.
9.
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.
10.
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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