Second-order linear differential equations



A second-order differential equation is an equation of the form
$$\frac{{{d^2}y}}{{d{t^2}}}\, = \,f\left( {t,y,\,\frac{{dy}}{{dt}}} \right)$$
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
$$\frac{{{d^2}y\left( t \right)}}{{d{t^2}}}\, = \,f\left( {t,y\left( t \right),\,\frac{{dy\left( t \right)}}{{dt}}} \right)$$


General Solution Homogeneous Equation Independent Solution Piecewise Continuous Function Indicial Equation 
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  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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