Author Topic: TUT0801 Quiz3  (Read 272 times)

bella

  • Newbie
  • *
  • Posts: 4
  • Karma: 0
    • View Profile
TUT0801 Quiz3
« 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. $W=1$