Answer :
Final answer:
The Wronskian of x₁ and x₂ is given by the formula: W(x₁, x₂) = x₁'x₂ - x₁x₂'
Explanation:
The Wronskian is a mathematical concept used to determine the linear independence of a set of functions. In this case, we are given the Wronskian of two functions, x₁ and x₂. The Wronskian of x₁ and x₂ is given by the formula:
W(x₁, x₂) = x₁'x₂ - x₁x₂'
where x₁' and x₂' represent the derivatives of x₁ and x₂, respectively.
To find the value of the Wronskian, we need to differentiate x₁ and x₂ and substitute the values into the formula. Let's assume x₁ = f(x) and x₂ = g(x).
Let's differentiate x₁ and x₂:
- x₁' = f'(x)
- x₂' = g'(x)
Substituting these values into the formula, we get:
W(x₁, x₂) = f'(x)g(x) - f(x)g'(x)
Now, we can evaluate the Wronskian using the given functions x₁ and x₂.
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