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MAT244-2013F
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MAT244 Math--Tests
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Quiz 2
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Problem 1, Night sections
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Topic: Problem 1, Night sections (Read 2998 times)
Victor Ivrii
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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.
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Yangming Cai
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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
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Tianqi Chen
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Re: Problem 1, Night sections
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Reply #2 on:
November 01, 2013, 11:22:46 AM »
Question1
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Victor Ivrii
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Re: Problem 1, Night sections
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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?
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Toronto Math Forum
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MAT244-2013F
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MAT244 Math--Tests
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Quiz 2
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Problem 1, Night sections