Toronto Math Forum
Welcome,
Guest
. Please
login
or
register
.
1 Hour
1 Day
1 Week
1 Month
Forever
Login with username, password and session length
News:
Home
Help
Search
Calendar
Login
Register
Toronto Math Forum
»
MAT244-2013F
»
MAT244 Math--Tests
»
Quiz 2
»
Problem 1, Night sections
« previous
next »
Print
Pages: [
1
]
Author
Topic: Problem 1, Night sections (Read 7092 times)
Victor Ivrii
Administrator
Elder Member
Posts: 2607
Karma: 0
Problem 1, Night sections
«
on:
October 30, 2013, 08:10:32 PM »
Assume that $p$ and $q$ are continuous and that the functions $y_1$ and $y_2$ are solutions of the differential equation
\begin{equation*}
y''+p(t)y'+q(t)y=0
\end{equation*}
on an open interval $I$.
Prove that if $y_1$ and $y_2$ are zero at the same point in $I$, then they cannot be a fundamental set of solutions on that interval.
Logged
Yangming Cai
Jr. Member
Posts: 12
Karma: 7
Re: Problem 1, Night sections
«
Reply #1 on:
October 30, 2013, 08:56:05 PM »
if $y_1$ and $y_2$ are zero at the same point in $I$ï¼Œthen its Wronskian , which is $y_1y_2'-y_2y_1'=0 $ and then $y_1$ and $y_2$ are not linearly independent, indicating that they cannot form a fundamental solution on that interval
«
Last Edit: October 31, 2013, 05:32:31 AM by Victor Ivrii
»
Logged
Tianqi Chen
Newbie
Posts: 2
Karma: 0
Re: Problem 1, Night sections
«
Reply #2 on:
November 01, 2013, 11:22:46 AM »
Question1
Logged
Victor Ivrii
Administrator
Elder Member
Posts: 2607
Karma: 0
Re: Problem 1, Night sections
«
Reply #3 on:
November 01, 2013, 04:28:08 PM »
Quote from: Tianqi Chen on November 01, 2013, 11:22:46 AM
Question1
What is the reason to post inferior (scanned) solution after a better -- typed has been posted?
Logged
Print
Pages: [
1
]
« previous
next »
Toronto Math Forum
»
MAT244-2013F
»
MAT244 Math--Tests
»
Quiz 2
»
Problem 1, Night sections