MAT244-2013F > Quiz 2

Problem 1, Night sections

(1/1)

**Victor Ivrii**:

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**:

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

**Tianqi Chen**:

Question1

**Victor Ivrii**:

--- Quote from: Tianqi Chen on November 01, 2013, 11:22:46 AM ---Question1

--- End quote ---

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

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