\[ x^2 \left (y'(x)^2+1\right )^3-a^2=0 \] ✓ Mathematica : cpu = 0.240722 (sec), leaf count = 406
\[\left \{\left \{y(x)\to c_1-\frac {\sqrt [3]{x} \left (2 x^{2/3}+\left (1+i \sqrt {3}\right ) a^{2/3}\right ) \sqrt {\frac {-2 x^{2/3}+\left (-1-i \sqrt {3}\right ) a^{2/3}}{x^{2/3}}}}{2 \sqrt {2}}\right \},\left \{y(x)\to c_1+\frac {\sqrt [3]{x} \sqrt {\frac {-2 x^{2/3}+\left (-1-i \sqrt {3}\right ) a^{2/3}}{x^{2/3}}} \left (2 x^{2/3}+\left (1+i \sqrt {3}\right ) a^{2/3}\right )}{2 \sqrt {2}}\right \},\left \{y(x)\to c_1-\frac {\sqrt [3]{x} \left (2 x^{2/3}+\left (1-i \sqrt {3}\right ) a^{2/3}\right ) \sqrt {\frac {-2 x^{2/3}+i \left (\sqrt {3}+i\right ) a^{2/3}}{x^{2/3}}}}{2 \sqrt {2}}\right \},\left \{y(x)\to c_1+\frac {\sqrt [3]{x} \sqrt {\frac {-2 x^{2/3}+i \left (\sqrt {3}+i\right ) a^{2/3}}{x^{2/3}}} \left (2 x^{2/3}+\left (1-i \sqrt {3}\right ) a^{2/3}\right )}{2 \sqrt {2}}\right \},\left \{y(x)\to \sqrt {\frac {a^{2/3}}{x^{2/3}}-1} \left (a^{2/3} \sqrt [3]{x}-x\right )+c_1\right \},\left \{y(x)\to \sqrt {\frac {a^{2/3}}{x^{2/3}}-1} \left (x-a^{2/3} \sqrt [3]{x}\right )+c_1\right \}\right \}\]
✓ Maple : cpu = 4.315 (sec), leaf count = 545
\[ \left \{ y \left ( x \right ) ={1\sqrt {-{\frac {1}{{a}^{4}} \left ( {a}^{2}x \right ) ^{{\frac {4}{3}}} \left ( \left ( {a}^{2}x \right ) ^{{\frac {2}{3}}}-{a}^{2} \right ) }} \left ( {a}^{2}- \left ( {a}^{2}x \right ) ^{{\frac {2}{3}}} \right ) \left ( {a}^{2}x \right ) ^{-{\frac {2}{3}}}}+{\it \_C1},y \left ( x \right ) ={1\sqrt {-{\frac {1}{{a}^{4}} \left ( {a}^{2}x \right ) ^{{\frac {4}{3}}} \left ( \left ( {a}^{2}x \right ) ^{{\frac {2}{3}}}-{a}^{2} \right ) }} \left ( \left ( {a}^{2}x \right ) ^{{\frac {2}{3}}}-{a}^{2} \right ) \left ( {a}^{2}x \right ) ^{-{\frac {2}{3}}}}+{\it \_C1},y \left ( x \right ) ={-{\frac {i}{4}}\sqrt {2} \left ( 2\,i \left ( {a}^{2}x \right ) ^{{\frac {2}{3}}}+ \left ( \sqrt {3}+i \right ) {a}^{2} \right ) \sqrt {{\frac {i}{{a}^{4}} \left ( {a}^{2}x \right ) ^{{\frac {4}{3}}} \left ( \sqrt {3}{a}^{2}+2\,i \left ( {a}^{2}x \right ) ^{{\frac {2}{3}}}+i{a}^{2} \right ) }} \left ( {a}^{2}x \right ) ^{-{\frac {2}{3}}}}+{\it \_C1},y \left ( x \right ) ={{\frac {i}{4}}\sqrt {2} \left ( 2\,i \left ( {a}^{2}x \right ) ^{{\frac {2}{3}}}+ \left ( \sqrt {3}+i \right ) {a}^{2} \right ) \sqrt {{\frac {i}{{a}^{4}} \left ( {a}^{2}x \right ) ^{{\frac {4}{3}}} \left ( \sqrt {3}{a}^{2}+2\,i \left ( {a}^{2}x \right ) ^{{\frac {2}{3}}}+i{a}^{2} \right ) }} \left ( {a}^{2}x \right ) ^{-{\frac {2}{3}}}}+{\it \_C1},y \left ( x \right ) ={-{\frac {i}{4}}\sqrt {2}\sqrt {-i \left ( \sqrt {3}\sqrt [3]{{a}^{2}x}-i\sqrt [3]{{a}^{2}x}-2\,ix \right ) x}\sqrt {{\frac {1}{{a}^{4}} \left ( {a}^{2}x \right ) ^{{\frac {4}{3}}} \left ( \sqrt {3}{a}^{2}-2\,i \left ( {a}^{2}x \right ) ^{{\frac {2}{3}}}-i{a}^{2} \right ) }} \left ( \sqrt {3}{a}^{2}-2\,i \left ( {a}^{2}x \right ) ^{{\frac {2}{3}}}-i{a}^{2} \right ) {\frac {1}{\sqrt { \left ( \sqrt {3}\sqrt [3]{{a}^{2}x}-i\sqrt [3]{{a}^{2}x}-2\,ix \right ) x}}} \left ( {a}^{2}x \right ) ^{-{\frac {2}{3}}}}+{\it \_C1},y \left ( x \right ) ={{\frac {i}{4}}\sqrt {2}\sqrt {-i \left ( \sqrt {3}\sqrt [3]{{a}^{2}x}-i\sqrt [3]{{a}^{2}x}-2\,ix \right ) x}\sqrt {{\frac {1}{{a}^{4}} \left ( {a}^{2}x \right ) ^{{\frac {4}{3}}} \left ( \sqrt {3}{a}^{2}-2\,i \left ( {a}^{2}x \right ) ^{{\frac {2}{3}}}-i{a}^{2} \right ) }} \left ( \sqrt {3}{a}^{2}-2\,i \left ( {a}^{2}x \right ) ^{{\frac {2}{3}}}-i{a}^{2} \right ) {\frac {1}{\sqrt { \left ( \sqrt {3}\sqrt [3]{{a}^{2}x}-i\sqrt [3]{{a}^{2}x}-2\,ix \right ) x}}} \left ( {a}^{2}x \right ) ^{-{\frac {2}{3}}}}+{\it \_C1} \right \} \]