Is the piecewise-defined function $$y = \left\lbrace \begin{array}{ll} -x^{2}, & \mbox{ if } x < 0 \\ x^{2}, & \mbox{ if } x \geq 0 \end{array} \right.$$ a solution of the differential equation $xy'-2y=0$ on $(-\infty,\infty)$?

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