# Toronto Math Forum

## MAT244-2013F => MAT244 Math--Tests => Quiz 2 => Topic started by: Victor Ivrii on October 30, 2013, 08:10:32 PM

Title: Problem 1, Night sections
Post by: Victor Ivrii 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.
Title: Re: Problem 1, Night sections
Post by: Yangming Cai 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
Title: Re: Problem 1, Night sections
Post by: Tianqi Chen on November 01, 2013, 11:22:46 AM
Question1
Title: Re: Problem 1, Night sections
Post by: Victor Ivrii on November 01, 2013, 04:28:08 PM
Question1

What is the reason to post inferior (scanned) solution after a better -- typed has been posted?