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Given $\cfrac{dy}{dx}=\cfrac{2x}{y},$ find the solution of the curve that goes through the point $(1, -1)$.

$y=-\sqrt {( { 2x }^{ 2 }-1 ) }$

$y=\sqrt {( { 2x }^{ 2 }-3 ) }$

$y=-\sqrt {( { 2x }^{ 2 }-3 ) }$

$y=\sqrt {( { 2x }^{ 2 }-1 ) }$