More generally, functions arose as solutions of ordinary differential equations (involving a function of one variable and its derivatives) and partial differential equations (involving a function of several variables and derivatives with respect to these variables).
Dilute solutions of strong acids for example, hydrochloric, sulfuric, and perchloric (HCl, H2SO4, HClO4 in water behave essentially as solutions of the ion H3O+, and their acidity increases in proportion to their concentration.
Polynomials are used as solutions of differential equations.
By Lemma 2.3, we have the critical points of as solutions of problem (3.19).
One also can see that the generating functions are determined as solutions of (2.23).
Also, they appear as solutions of many important ordinary differential equations [7, 11, 20].
Therefore, it is natural to seek these solutions as solutions of ordinary differential equations.
These vacua are either viewed as distinct string theories, or else as solutions of one and the same theory (though some deeper, unknown theory, as mentioned above).
Then we define mathematically this problem, and we obtain the reach probabilities as solutions of a boundary value problem.
We will consider solutions of problem (1.1) as solutions of the following parabolic problem with multivalued right-hand side: (17).
It follows that magnetic geodesics cannot be extended, as solutions of the magnetic geodesic equation, into singular points.
