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Unformatted text preview: Notes for Day : § . : Introduction to Second Order Linear Di erentia Equations We now advance our focus from rstorder to secondorder equations. Chapter covers only linear secondorder equations. Much of the work we invested in studying linear rstorder equations will carry over. Secondorder equations: What stays the same (or near y the same)? Every linear secondorder equation can be written in the standard form: y ′′ + p ( t ) y ′ + q ( t ) y = g ( t ) If g ( t ) = , we will continue to say that the di erential equation is “homogeneous”. eorem . gives us a method for identifying the largest interval where a unique solution is guaranteed to exist: Existence and Uniqueness for Second Order Linear Initia Va ue Prob ems Let p ( t ) , q ( t ) and g ( t ) be functions which are continuous on an interval ( a , b ) , and let t be in the interval ( a , b ) . en a solution to the initial value problem y ′′ + p ( t ) y ′ + q ( t ) y = g ( t ) , y ( t ) = y , y ′ ( t ) = y ′ exists and is unique on the interval ( a , b ) ....
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This note was uploaded on 04/05/2008 for the course MATH 2214 taught by Professor Edesturler during the Spring '06 term at Virginia Tech.
 Spring '06
 EDeSturler
 Equations

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