MAT244--2018F > Quiz-3
Q3 TUT 0201
(1/1)
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 $xe^{x}$
$$W(x, xe^x) = \left|\begin{matrix}x & xe^{x} \\ x' & (xe^{x})'\end{matrix}\right|= \left|\begin{matrix}x & xe^{x} \\ 1 & xe^{x}+e^{x}\end{matrix}\right| = x^{2}e^{x}+xe^{x}-xe^{x}=x^{2}e^{x}.$$
Navigation
[0] Message Index
Go to full version