\[ \left (a \left (x^2+y(x)^2\right )^{3/2}-x^2\right ) y'(x)^2+a \left (x^2+y(x)^2\right )^{3/2}+2 x y(x) y'(x)-y(x)^2=0 \] ✓ Mathematica : cpu = 4.94721 (sec), leaf count = 713
\[\left \{\text {Solve}\left [\tan ^{-1}\left (\frac {x}{y(x)}\right )-\frac {i \sqrt {a \left (\left (x^2+y(x)^2\right )^{5/2}-a \left (x^2+y(x)^2\right )^3\right )} \left (\sqrt {2} \left (\log \left (\frac {a^{3/2} \left (3 i \sqrt {2} a \sqrt {x^2+y(x)^2}+4 \sqrt {a} \sqrt {\sqrt {x^2+y(x)^2}-a \left (x^2+y(x)^2\right )}-i \sqrt {2}\right )}{4 a \sqrt {x^2+y(x)^2}+4}\right )-\log \left (\frac {-3 i \sqrt {2} a^{3/2} \sqrt {x^2+y(x)^2}-4 a \sqrt {\sqrt {x^2+y(x)^2}-a \left (x^2+y(x)^2\right )}+i \sqrt {2} \sqrt {a}}{4 a \sqrt {x^2+y(x)^2}+4}\right )\right )+2 \log \left (\frac {-2 i a \sqrt {x^2+y(x)^2}+2 \sqrt {a} \sqrt {\sqrt {x^2+y(x)^2}-a \left (x^2+y(x)^2\right )}+i}{\sqrt {a}}\right )\right )}{2 \sqrt {a} \left (x^2+y(x)^2\right ) \sqrt {\sqrt {x^2+y(x)^2}-a \left (x^2+y(x)^2\right )}}=c_1,y(x)\right ],\text {Solve}\left [\tan ^{-1}\left (\frac {x}{y(x)}\right )+\frac {i \sqrt {a \left (\left (x^2+y(x)^2\right )^{5/2}-a \left (x^2+y(x)^2\right )^3\right )} \left (\sqrt {2} \left (\log \left (\frac {a^{3/2} \left (3 i \sqrt {2} a \sqrt {x^2+y(x)^2}+4 \sqrt {a} \sqrt {\sqrt {x^2+y(x)^2}-a \left (x^2+y(x)^2\right )}-i \sqrt {2}\right )}{4 a \sqrt {x^2+y(x)^2}+4}\right )-\log \left (\frac {-3 i \sqrt {2} a^{3/2} \sqrt {x^2+y(x)^2}-4 a \sqrt {\sqrt {x^2+y(x)^2}-a \left (x^2+y(x)^2\right )}+i \sqrt {2} \sqrt {a}}{4 a \sqrt {x^2+y(x)^2}+4}\right )\right )+2 \log \left (\frac {-2 i a \sqrt {x^2+y(x)^2}+2 \sqrt {a} \sqrt {\sqrt {x^2+y(x)^2}-a \left (x^2+y(x)^2\right )}+i}{\sqrt {a}}\right )\right )}{2 \sqrt {a} \left (x^2+y(x)^2\right ) \sqrt {\sqrt {x^2+y(x)^2}-a \left (x^2+y(x)^2\right )}}=c_1,y(x)\right ]\right \}\] ✓ Maple : cpu = 6.143 (sec), leaf count = 135
\[ \left \{ y \left ( x \right ) ={x \left ( \tan \left ( {\it RootOf} \left ( -{\it \_Z}+\int ^{{\frac {{x}^{2} \left ( \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}+1 \right ) }{ \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}}}}\!-{\frac {1}{2\,{{\it \_a}}^{2} \left ( {\it \_a}\,{a}^{2}-1 \right ) }\sqrt {-{{\it \_a}}^{{\frac {5}{2}}}a \left ( \sqrt {{\it \_a}}a-1 \right ) } \left ( \sqrt {{\it \_a}}a+1 \right ) }{d{\it \_a}}+{\it \_C1} \right ) \right ) \right ) ^{-1}},y \left ( x \right ) ={x \left ( \tan \left ( {\it RootOf} \left ( -{\it \_Z}+\int ^{{\frac {{x}^{2} \left ( \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}+1 \right ) }{ \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}}}}\!{\frac {1}{2\,{{\it \_a}}^{2} \left ( {\it \_a}\,{a}^{2}-1 \right ) }\sqrt {-{{\it \_a}}^{{\frac {5}{2}}}a \left ( \sqrt {{\it \_a}}a-1 \right ) } \left ( \sqrt {{\it \_a}}a+1 \right ) }{d{\it \_a}}+{\it \_C1} \right ) \right ) \right ) ^{-1}} \right \} \]