Question

Find the Wronskian of the following pair of functions: {3t, 2t}.

A) 3t

B) 6t

C) 2

D) 0

Answer 1

The Wronskian of the functions {3t, 2t} is calculated as 0, indicating that the functions are linearly dependent.

Step-by-step explanation:

The Wronskian of a pair of functions is a determinant used in the theory of differential equations to determine if a set of solutions is linearly independent. For a pair of functions f(t) = 3t and g(t) = 2t, the Wronskian W(f,g) is calculated using the following formula:

W(f,g) = f(t)g'(t) - f'(t)g(t)

Where f'(t) and g'(t) are the derivatives of f(t) and g(t), respectively. For the given functions:

• f'(t) = 3
• g'(t) = 2

Substituting these into the Wronskian formula, we get:

W(3t, 2t) = (3t)(2) - (3)(2t) = 6t - 6t = 0

Thus, the Wronskian of the function pair {3t, 2t} is 0, which corresponds to answer choice D. This indicates that the functions are linearly dependent.