Answer
Yes
Work Step by Step
$xy'-2y=x^{3}ex$
$y=x^{2}e^{x}, y'=x^{2}e^{x}+2e^{x}$
$y'=e^{x}(x^{2}+2x)$
$xy'-2y=x(e^{x}(x^{2}+2x))-2(x^{2}e^{x})$
$x(e^{x}(x^{2}+2x))-2(x^{2}e^{x})$=$x^{3}e^{x}$
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