\[ x^2 \left (y'(x)^2+1\right )^3-a^2=0 \] ✓ Mathematica : cpu = 0.252285 (sec), leaf count = 216
\[\left \{\left \{y(x)\to -x \left (\frac {a^{2/3}}{x^{2/3}}-1\right )^{3/2}+c_1\right \},\left \{y(x)\to x \left (\frac {a^{2/3}}{x^{2/3}}-1\right )^{3/2}+c_1\right \},\left \{y(x)\to c_1-x \left (-1-\frac {i \left (\sqrt {3}-i\right ) a^{2/3}}{2 x^{2/3}}\right )^{3/2}\right \},\left \{y(x)\to x \left (-1-\frac {i \left (\sqrt {3}-i\right ) a^{2/3}}{2 x^{2/3}}\right )^{3/2}+c_1\right \},\left \{y(x)\to c_1-x \left (-1+\frac {i \left (\sqrt {3}+i\right ) a^{2/3}}{2 x^{2/3}}\right )^{3/2}\right \},\left \{y(x)\to x \left (-1+\frac {i \left (\sqrt {3}+i\right ) a^{2/3}}{2 x^{2/3}}\right )^{3/2}+c_1\right \}\right \}\] ✓ Maple : cpu = 0.758 (sec), leaf count = 553
\[\left \{y \left (x \right ) = c_{1}+\frac {\sqrt {-\frac {\left (a^{2} x \right )^{\frac {4}{3}} \left (-a^{2}+\left (a^{2} x \right )^{\frac {2}{3}}\right )}{a^{4}}}\, \left (a^{2}-\left (a^{2} x \right )^{\frac {2}{3}}\right )}{\left (a^{2} x \right )^{\frac {2}{3}}}, y \left (x \right ) = c_{1}+\frac {\sqrt {-\frac {\left (a^{2} x \right )^{\frac {4}{3}} \left (-a^{2}+\left (a^{2} x \right )^{\frac {2}{3}}\right )}{a^{4}}}\, \left (-a^{2}+\left (a^{2} x \right )^{\frac {2}{3}}\right )}{\left (a^{2} x \right )^{\frac {2}{3}}}, y \left (x \right ) = c_{1}-\frac {i \left (\left (\sqrt {3}+i\right ) a^{2}+2 i \left (a^{2} x \right )^{\frac {2}{3}}\right ) \sqrt {2}\, \sqrt {\frac {i \left (a^{2} x \right )^{\frac {4}{3}} \left (i a^{2}+\sqrt {3}\, a^{2}+2 i \left (a^{2} x \right )^{\frac {2}{3}}\right )}{a^{4}}}}{4 \left (a^{2} x \right )^{\frac {2}{3}}}, y \left (x \right ) = c_{1}+\frac {i \left (\left (\sqrt {3}+i\right ) a^{2}+2 i \left (a^{2} x \right )^{\frac {2}{3}}\right ) \sqrt {2}\, \sqrt {\frac {i \left (a^{2} x \right )^{\frac {4}{3}} \left (i a^{2}+\sqrt {3}\, a^{2}+2 i \left (a^{2} x \right )^{\frac {2}{3}}\right )}{a^{4}}}}{4 \left (a^{2} x \right )^{\frac {2}{3}}}, y \left (x \right ) = c_{1}-\frac {i \sqrt {2}\, \sqrt {i \left (2 i x +i \left (a^{2} x \right )^{\frac {1}{3}}-\sqrt {3}\, \left (a^{2} x \right )^{\frac {1}{3}}\right ) x}\, \sqrt {\frac {\left (a^{2} x \right )^{\frac {4}{3}} \left (i a^{2}-\sqrt {3}\, a^{2}+2 i \left (a^{2} x \right )^{\frac {2}{3}}\right )}{a^{4}}}\, \left (i a^{2}-\sqrt {3}\, a^{2}+2 i \left (a^{2} x \right )^{\frac {2}{3}}\right )}{4 \sqrt {\left (2 i x +i \left (a^{2} x \right )^{\frac {1}{3}}-\sqrt {3}\, \left (a^{2} x \right )^{\frac {1}{3}}\right ) x}\, \left (a^{2} x \right )^{\frac {2}{3}}}, y \left (x \right ) = c_{1}+\frac {i \sqrt {2}\, \sqrt {i \left (2 i x +i \left (a^{2} x \right )^{\frac {1}{3}}-\sqrt {3}\, \left (a^{2} x \right )^{\frac {1}{3}}\right ) x}\, \sqrt {\frac {\left (a^{2} x \right )^{\frac {4}{3}} \left (i a^{2}-\sqrt {3}\, a^{2}+2 i \left (a^{2} x \right )^{\frac {2}{3}}\right )}{a^{4}}}\, \left (i a^{2}-\sqrt {3}\, a^{2}+2 i \left (a^{2} x \right )^{\frac {2}{3}}\right )}{4 \sqrt {\left (2 i x +i \left (a^{2} x \right )^{\frac {1}{3}}-\sqrt {3}\, \left (a^{2} x \right )^{\frac {1}{3}}\right ) x}\, \left (a^{2} x \right )^{\frac {2}{3}}}\right \}\]