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Unformatted text preview: Notes for Day : § . : Introduction to Second Order Linear Di erentia Equations We now advance our focus from rst-order to second-order equations. Chapter covers only linear second-order equations. Much of the work we invested in studying linear rst-order equations will carry over. Second-order equations: What stays the same (or near y the same)? Every linear second-order 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