Find the Wronskian of the functions $f(t)=6e^t\sin{t}$ and $g(t)=e^t\cos(t)$. Simplify your answer. please list out all steps as simple as possible thank you
2026-02-23 13:44:37.1771854277
Find the Wronskian of the Functions
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Recall, that given $$f(t)=6e^t\sin{t}\quad g(t)=e^t\cos(t)$$
The Wronskian of $f(t), g(t) = W(f,g)(t)$
$$W(f, g)(t) =\det \left(\begin{bmatrix}f(t) & g(t) \\ f'(t) & g'(t) \end{bmatrix}\right)$$
So find each of $f'(t)$ and $g'(t)$, and substitute $f, g, f', g'$ into the matrix; then you simply compute the determinant: $$W(f, g)(t)= f(t)\cdot g'(t) - f'(t)\cdot g(t)$$