e Elementary Differential X1G Calculus question! Che y wileyPLUS CSecure https:/

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e Elementary Differential X1G Calculus question! Che y wileyPLUS CSecure https://edugen.wileyplus.com/edugen/student/mainfr.uni WileyPLUS: MyWlleyPLUS I 1 Help Contact Us | Log Out WileyPLUS Boyce/DiPrima, Differential Equations and Boundary Value problems, 1oth Edition Boyce/DiPrima, Differential Equations and Boundary Value Problems, 10th Edition DIFFERENTIAL EQUATIONS (MATH 350) Home Read, Study & Practice Gradebook Downloadable eTextbook Assignment>Open Assignment FULL SCREEN PRINTER VERSION BACK NEXT ASSIGNMENT RESOURCES Chapter 5, Section 5.3, Question 08 5.1-5.3 Homework Determine a lower bound for the radius of convergence of series solutions about the given point X0 for the given differential equation. Chanten SacionS2.Enter ir the Enter r the series solutions converge everywhere. lick here to enter or edit your answer hapter 5, Se

Explanation / Answer

given

xy'' + 2 y = 0 , x0=6

write the equation in standard form

y'' + ( 2/x) y = 0

We see that the singular points are solutions to

x = 0 ,so given equation is undefined at x = 0

the distance between expansion point and singularity is

dist ( 6, 0 ) ==> sqrt( 6^2 + 0^2 )==> 6

hence the distance between expansion point and closet singularity is 6

so the radius of convergence of power series solution about at point x0=6 will be atleat 6

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