Author Topic: TUT0102 Quiz3  (Read 298 times)

Changhao Jiang

  • Jr. Member
  • **
  • Posts: 8
  • Karma: 0
    • View Profile
TUT0102 Quiz3
« on: October 11, 2019, 02:03:03 PM »
\documentclass{article}
\usepackage[utf8]{inputenc}


\usepackage{natbib}
\usepackage{graphicx}
\usepackage{amsmath}
\begin{document}


If the Wronskian W of f and g is $3e^{4t}$, and if $f(t)=e^{2t}$, find g(t)

Solution: We calculate the Wronskian of f and g:

$W =
\begin{vmatrix}
f(t) & g(t) \\
f'(t) & g'(t) \\
\end{vmatrix}
=
\begin{vmatrix}
e^{2t} & g(t) \\
2e^{2t} & g'(t) \\
\end{vmatrix} $
= $e^{2t}g'(t)-2e^{2t}g(t)=3e^{4t}$ \newline
$e^{2t}g'(t)-2e^{2t}g(t)=3e^{4t}$ \newline