Abstract
This chapter discusses differential equations and nonlinear equations. Except for a few special cases, there is no systematic theory of solutions of nonlinear equations by quadratures or by a finite mathematical construction. The ultimate aim in studying differentiable equations does not consist only of finding local solutions in a neighborhood of a point or even in a given interval but also of finding a complete characterization of the global behavior of the family of solutions. This is possible even for equations that cannot be readily represented by explicit formulas. This problem is still not completely solved until present. Even in the case of simple linear equations with constant coefficients, this problem is nontrivial and of great help in obtaining a better insight into the nature of differential equations. A different aspect of the global behavior of solutions of differential equations is their relative position to one another or their stability that plays an important part in applications.
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