\[ y'(x)=\frac {4 (a-1) (a+1) x \left (a^2 x^2-x^2-y(x)^2-2\right )}{-3 a^6 x^4 y(x)^2+3 a^4 x^2 y(x)^4+9 a^4 x^4 y(x)^2-6 a^2 x^2 y(x)^4-9 a^2 x^4 y(x)^2+4 a^2 x^2 y(x)+a^8 x^6-4 a^6 x^6+6 a^4 x^6-4 a^2 x^6-a^2 y(x)^6+3 x^2 y(x)^4+3 x^4 y(x)^2-4 x^2 y(x)+x^6+y(x)^6-4 y(x)^3-8 y(x)} \] ✓ Mathematica : cpu = 4.78607 (sec), leaf count = 1191
\[\left \{\left \{y(x)\to \text {Root}\left [2 x^4 a^8-8 x^4 a^6+e^{c_1} x^4 a^4+11 x^4 a^4-2 e^{c_1} x^4 a^2-6 x^4 a^2+4 x^2 a^2+\left (2 a^2-2\right ) \text {$\#$1}^5+e^{c_1} x^4+x^4+\left (2 a^4-4 a^2+e^{c_1}+1\right ) \text {$\#$1}^4+\left (-4 x^2 a^4+8 x^2 a^2-4 x^2\right ) \text {$\#$1}^3-4 x^2+\left (-4 x^2 a^6+12 x^2 a^4-2 e^{c_1} x^2 a^2-10 x^2 a^2+2 e^{c_1} x^2+2 x^2-4\right ) \text {$\#$1}^2+\left (2 x^4 a^6-6 x^4 a^4+6 x^4 a^2-2 x^4\right ) \text {$\#$1}-4\& ,1\right ]\right \},\left \{y(x)\to \text {Root}\left [2 x^4 a^8-8 x^4 a^6+e^{c_1} x^4 a^4+11 x^4 a^4-2 e^{c_1} x^4 a^2-6 x^4 a^2+4 x^2 a^2+\left (2 a^2-2\right ) \text {$\#$1}^5+e^{c_1} x^4+x^4+\left (2 a^4-4 a^2+e^{c_1}+1\right ) \text {$\#$1}^4+\left (-4 x^2 a^4+8 x^2 a^2-4 x^2\right ) \text {$\#$1}^3-4 x^2+\left (-4 x^2 a^6+12 x^2 a^4-2 e^{c_1} x^2 a^2-10 x^2 a^2+2 e^{c_1} x^2+2 x^2-4\right ) \text {$\#$1}^2+\left (2 x^4 a^6-6 x^4 a^4+6 x^4 a^2-2 x^4\right ) \text {$\#$1}-4\& ,2\right ]\right \},\left \{y(x)\to \text {Root}\left [2 x^4 a^8-8 x^4 a^6+e^{c_1} x^4 a^4+11 x^4 a^4-2 e^{c_1} x^4 a^2-6 x^4 a^2+4 x^2 a^2+\left (2 a^2-2\right ) \text {$\#$1}^5+e^{c_1} x^4+x^4+\left (2 a^4-4 a^2+e^{c_1}+1\right ) \text {$\#$1}^4+\left (-4 x^2 a^4+8 x^2 a^2-4 x^2\right ) \text {$\#$1}^3-4 x^2+\left (-4 x^2 a^6+12 x^2 a^4-2 e^{c_1} x^2 a^2-10 x^2 a^2+2 e^{c_1} x^2+2 x^2-4\right ) \text {$\#$1}^2+\left (2 x^4 a^6-6 x^4 a^4+6 x^4 a^2-2 x^4\right ) \text {$\#$1}-4\& ,3\right ]\right \},\left \{y(x)\to \text {Root}\left [2 x^4 a^8-8 x^4 a^6+e^{c_1} x^4 a^4+11 x^4 a^4-2 e^{c_1} x^4 a^2-6 x^4 a^2+4 x^2 a^2+\left (2 a^2-2\right ) \text {$\#$1}^5+e^{c_1} x^4+x^4+\left (2 a^4-4 a^2+e^{c_1}+1\right ) \text {$\#$1}^4+\left (-4 x^2 a^4+8 x^2 a^2-4 x^2\right ) \text {$\#$1}^3-4 x^2+\left (-4 x^2 a^6+12 x^2 a^4-2 e^{c_1} x^2 a^2-10 x^2 a^2+2 e^{c_1} x^2+2 x^2-4\right ) \text {$\#$1}^2+\left (2 x^4 a^6-6 x^4 a^4+6 x^4 a^2-2 x^4\right ) \text {$\#$1}-4\& ,4\right ]\right \},\left \{y(x)\to \text {Root}\left [2 x^4 a^8-8 x^4 a^6+e^{c_1} x^4 a^4+11 x^4 a^4-2 e^{c_1} x^4 a^2-6 x^4 a^2+4 x^2 a^2+\left (2 a^2-2\right ) \text {$\#$1}^5+e^{c_1} x^4+x^4+\left (2 a^4-4 a^2+e^{c_1}+1\right ) \text {$\#$1}^4+\left (-4 x^2 a^4+8 x^2 a^2-4 x^2\right ) \text {$\#$1}^3-4 x^2+\left (-4 x^2 a^6+12 x^2 a^4-2 e^{c_1} x^2 a^2-10 x^2 a^2+2 e^{c_1} x^2+2 x^2-4\right ) \text {$\#$1}^2+\left (2 x^4 a^6-6 x^4 a^4+6 x^4 a^2-2 x^4\right ) \text {$\#$1}-4\& ,5\right ]\right \}\right \}\] ✓ Maple : cpu = 1.257 (sec), leaf count = 79
\[ \left \{ -{\frac {y \left ( x \right ) }{ \left ( a-1 \right ) \left ( a+1 \right ) }}+2\,{\frac {1}{ \left ( {a}^{2}-1 \right ) ^{2} \left ( {a}^{2}{x}^{2}-{x}^{2}- \left ( y \left ( x \right ) \right ) ^{2} \right ) ^{2}}}-2\,{\frac {1}{ \left ( {a}^{2}-1 \right ) ^{2} \left ( {a}^{2}{x}^{2}-{x}^{2}- \left ( y \left ( x \right ) \right ) ^{2} \right ) }}+{\it \_C1}=0 \right \} \]