Question

1) The Wronskian of the function y, = sinx and y, = sinx - cosx is --
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Answer 1

Answer:

ok

Step-by-step explanation:

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Answer 2

Concept:

We need to recall the concept of wronskian in differential equations to solve this question.

• Wronskian is the determinant used in differential equations.

• Wronskian of two diffferentiable function f(x) and g(x) is given by:

• W ( f , g ) = f g' - g f' .

      i.e., Determinant constructed by placing the functions in first row, the          

      first derivative of function in next row , for two function and forms a  

      square matrix.

Given:

The two functions : $y_{1} = sinx$ and $y_{2} = sinx - cos x$ .

To find:

The wronskian of two functions.

Solution:

The wronskian is given by :

W = $\begin{vmatrix} y_{1}&y_{2} \\ y_{1}' & y_{2}'\end{vmatrix}$

    =  $y_{1}y_{2}' - y_{2}y_{1}'$

Given, $y_{1} = sinx$ and  $y_{2} = sinx - cos x$

 so,     $y_{1}' = cosx$  and $y_{2} '= cosx+sinx$

           W = sin x (cos x + sin x) - ( sin x - cos x) cos x

               = sin x cos x + $sin^{2}x$ -sin x cos x + $cos^{2}x$

               = $sin^{2}x$ + $cos^{2}x$                                       (  as  $sin^{2}x$ + $cos^{2}x$ = 1)

               = 1

Hence, wronskian of the given functions is 1.