Toronto Math Forum
MAT2442019F => MAT244Test & Quizzes => Quiz3 => Topic started by: bella on October 11, 2019, 02:05:09 PM

Find the Wronskian of the given pair of functions.
$$
\cos (t), \sin (t);
$$
Suppose $y_{1}(t)=\cos t$, $y_{2}(t)=\sin t$
Then Wronskian for this pair is given by
$W\left(y_{1}, y_{2}\right)=\left\begin{array}{cc}{y_{1}(t)} & {y_{2}(t)} \\ {y_{1}^{\prime}(t)} & {y_{2}^{\prime}(t)}\end{array}\right$
$=\left\begin{array}{cc}{\cos t} & {\sin t} \\ {\sin t} & {\cos t}\end{array}\right$
$=\cos ^{2} t+\sin ^{2} t$
$=1$
i.e. $W=1$