### Author Topic: Problem 1, Night sections  (Read 4431 times)

#### Victor Ivrii

• Elder Member
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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.

#### Yangming Cai

• Jr. Member
• Posts: 12
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##### 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 »

#### Tianqi Chen

• Newbie
• Posts: 2
• Karma: 0
##### Re: Problem 1, Night sections
« Reply #2 on: November 01, 2013, 11:22:46 AM »
Question1