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In the study of differential equations, methods from all fields of mathematics are used. In this chapter, we discuss selected special equations and types of equation. Special attention is paid, on the one hand, to the significance in applications of these equations and, on the other hand, to the connection between research methods and various general mathematical problems (resolution of singularities, Newton diagrams, Lie groups of symmetries, etc.). This chapter concludes with the elementary theory of the one-dimensional stationary Schrödinger equation and the geometric theory of a nonlinear equation of the second order.
KeywordsDirection Field Integral Curve Projective Transformation Integral Curf Special Equation
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