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MAT244--2019F => MAT244--Test & Quizzes => Quiz-3 => Topic started by: bella on October 11, 2019, 02:05:09 PM

Title: TUT0801 Quiz3
Post 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. $W=1$