All Questions Topic List
Others Questions
Previous in All Question Next in All Question
Previous in Others Next in Others
Question Number 184307 by Mastermind last updated on 05/Jan/23
Showthattheboundary−value problemy″+λy=0y(0)=0, y(L)=0hasonlythetrivalsolution y=0forthecasesλ=0andλ<0. letLbeanon−zerorealnumber. ?
Answered by FelipeLz last updated on 05/Jan/23
y″+λy=0 y=er→r2er+λer=0 r2=−λ λ=0→r=0∴y(x)=c y(0)=0=c y(x)=0 λ<0→r=±−λ∴y(x)=c1e−λx+c2e−−λx y(0)=0→c1+c2=0∴y(x)=c(e−λx−e−−λx) y(L)=0→c(e−λL−e−−λL)=0 L≠0→e−λL−e−−λL≠0∴c=0 y(x)=0
Terms of Service
Privacy Policy
Contact: info@tinkutara.com