MAT244--2018F > Quiz-3

Q3 TUT 0201

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Victor Ivrii:
Find the Wronskian of the given pair of functions: $x$ and $xe^x$.

Pengyun Li:
$W(x, xe^x) = \left|\begin{matrix}x & xe^x \\ x' & (xe^x)'\end{matrix}\right|= \left|\begin{matrix}x & xe^x \\ 1 & x^2e^x+e^x\end{matrix}\right| = x(x^2e^x+e^x) - xe^x = x^3e^x$

Victor Ivrii:
Who taught you differentiate like this?!

Monika Dydynski:
(Pengyun's solution with corrected derivative of $xe^{x}$)

Find the Wronskian of the given pair of functions: $x$ and $xe^{x}$

$$W(x, xe^x) = \left|\begin{matrix}x & xe^{x} \\ x' & (xe^{x})'\end{matrix}\right|= \left|\begin{matrix}x & xe^{x} \\ 1 & xe^{x}+e^{x}\end{matrix}\right| = x^{2}e^{x}+xe^{x}-xe^{x}=x^{2}e^{x}.$$