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Second-order linear differential equations

Chapter

Abstract

A second-order differential equation is an equation of the form
$$\frac{{{d^2}y}}{{d{t^2}}}\, = \,f\left( {t,y,\,\frac{{dy}}{{dt}}} \right)$$
(1)
For example, the equation
$$\frac{{{d^2}y}}{{d{t^2}}}\, = \,\sin t\, + \,3y\, + \,{\left( {\frac{{dy}}{{dt}}} \right)^2}$$
is a second-order differential equation. A function y = y(t) is a solution of (1) if y(t) satisfies the differential equation; that is
$$\frac{{{d^2}y\left( t \right)}}{{d{t^2}}}\, = \,f\left( {t,y\left( t \right),\,\frac{{dy\left( t \right)}}{{dt}}} \right)$$
.

Keywords

General Solution Homogeneous Equation Independent Solution Piecewise Continuous Function Indicial Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Reference

  1. E. Ackerman, L. Gatewood, J. Rosevear, and G. Molnar, Blood glucose regulation and diabetes, Chapter 4 in Concepts and Models of Biomathematics, F. Heinmets, ed., Marcel Dekker, 1969, 131–156.Google Scholar

Copyright information

© Springer-Verlag, New York Inc. 1978

Authors and Affiliations

  1. 1.Department of Mathematics Queens CollegeCity University of New YorkFlushingUSA

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