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On the Eigenvalues of Differential Equations
American Journal of Mathematics, 1951is the t-value satisfying q (t) S. The assumption of the existence of a third derivative, as pointed out by Milne, was unessential to his proof. Titchmarsh [5] gave a simplified proof of (4) retaining all of Milne's conditions, except that concerning the existence of a third derivative.
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Ordinary Differential Equations
2012In this chapter we provide an overview of the basic theory of ordinary differential equations (ODE). We give the basics of analytical methods for their solutions and also review numerical methods. The chapter should serve as a primer for the basic application of ODEs and systems of ODEs in practice.
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Systems of differential equations
1975In this chapter we will consider simultaneous first-order differential equations in several variables, that is, equations of the form $$\begin{gathered} \frac{{d{x_1}}}{{dt}} = {f_1}\left( {t,{x_1},...,{x_n}} \right), \hfill \\ \frac{{d{x_2}}}{{dt}} = {f_2}\left( {t,{x_1},...,{x_n}} \right), \hfill \\ \vdots \hfill \\ \frac{{d{x_n}}}{{dt}} = {f_n ...
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Quantizations of differential equations
Nonlinear Analysis: Theory, Methods & Applications, 2001openaire +2 more sources