Question

If y_1=Cos 3x and y_2=Sin 3x are two solutions then W = ….. *
1​

Answer 1

SOLUTION

GIVEN

The solution is given by

$\sf{y_1 = \cos 3x \: \: \: and \: \: \: y_2 = \sin 3x}$

TO DETERMINE

The value of W

EVALUATION

Here it is given that the solution is given by

$\sf{y_1 = \cos 3x \: \: \: and \: \: \: y_2 = \sin 3x}$

Hence the required Wronskian

= W

$= \displaystyle \sf{\begin{vmatrix} \: \: y_1 & y_2 \\ \\ y_1' & y_2' \: \: \end{vmatrix} }$

$= \displaystyle \sf{\begin{vmatrix} \: \sf{\cos 3x} & \sf{\sin 3x} \\ \\ - 3\sf{\sin 3x} & 3\sf{\cos 3x} \: \: \end{vmatrix} }$

$= \sf{3{\cos}^{2} 3x +3{\sin}^{2} 3x }$

$= \sf{3({\cos}^{2} 3x +{\sin}^{2} 3x) }$

$= \sf{3 \times 1 }$

$= 3$

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