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Find the solution of $y'=\cfrac { 2{ x }^{ 3 } }{ 2y+1 } $, given that $x=2$ when $y=0$.

${ y }^{ 2 }+\cfrac { 1 }{ 2 } { x }^{ 4 }=8$

${ y }^{ 2 }+y+{ x }^{ 4 }=2$

${ y }^{ 2 }+y-\cfrac { 1 }{ 2 } { x }^{ 4 }=-8$

$\cfrac { 1 }{ 2 } { y }^{ 2 }+x=-8$