\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =2\,{\frac { \left ( y \left ( x \right ) \right ) ^{6} \left ( 1+4\,x \left ( y \left ( x \right ) \right ) ^{2}+ \left ( y \left ( x \right ) \right ) ^{2} \right ) }{ \left ( y \left ( x \right ) \right ) ^{3}+4\, \left ( y \left ( x \right ) \right ) ^{5}x+ \left ( y \left ( x \right ) \right ) ^{5}+2+24\,x \left ( y \left ( x \right ) \right ) ^{2}+96\,{x}^{2} \left ( y \left ( x \right ) \right ) ^{4}+128\,{x}^{3} \left ( y \left ( x \right ) \right ) ^{6}}}=0} \]
Mathematica: cpu = 0.244531 (sec), leaf count = 301 \[ \left \{\left \{y(x)\to \text {Root}\left [\text {$\#$1}^5 \left (128 c_1 x^2-8 x-1\right )+128 \text {$\#$1}^4 x^2+\text {$\#$1}^3 \left (64 c_1 x-2\right )+64 \text {$\#$1}^2 x+8 \text {$\#$1} c_1+8\& ,1\right ]\right \},\left \{y(x)\to \text {Root}\left [\text {$\#$1}^5 \left (128 c_1 x^2-8 x-1\right )+128 \text {$\#$1}^4 x^2+\text {$\#$1}^3 \left (64 c_1 x-2\right )+64 \text {$\#$1}^2 x+8 \text {$\#$1} c_1+8\& ,2\right ]\right \},\left \{y(x)\to \text {Root}\left [\text {$\#$1}^5 \left (128 c_1 x^2-8 x-1\right )+128 \text {$\#$1}^4 x^2+\text {$\#$1}^3 \left (64 c_1 x-2\right )+64 \text {$\#$1}^2 x+8 \text {$\#$1} c_1+8\& ,3\right ]\right \},\left \{y(x)\to \text {Root}\left [\text {$\#$1}^5 \left (128 c_1 x^2-8 x-1\right )+128 \text {$\#$1}^4 x^2+\text {$\#$1}^3 \left (64 c_1 x-2\right )+64 \text {$\#$1}^2 x+8 \text {$\#$1} c_1+8\& ,4\right ]\right \},\left \{y(x)\to \text {Root}\left [\text {$\#$1}^5 \left (128 c_1 x^2-8 x-1\right )+128 \text {$\#$1}^4 x^2+\text {$\#$1}^3 \left (64 c_1 x-2\right )+64 \text {$\#$1}^2 x+8 \text {$\#$1} c_1+8\& ,5\right ]\right \}\right \} \]
Maple: cpu = 0 (sec), leaf count = 0 \[ \text {hanged} \]