\[ \left (y(x)^4-a^2 x^2\right ) y'(x)^2+2 a^2 x y(x) y'(x)+y(x)^2 \left (y(x)^2-a^2\right )=0 \] ✓ Mathematica : cpu = 29.2635 (sec), leaf count = 443
\[\left \{\text {Solve}\left [\left \{x=\frac {a^2 \text {K$\$$19743} y(\text {K$\$$19743})-\sqrt {a^2 \text {K$\$$19743}^2 \left (\text {K$\$$19743}^2+1\right ) y(\text {K$\$$19743})^4}}{a^2 \text {K$\$$19743}^2},y(x)=\frac {1}{4} \left (-\frac {a c_1 \sqrt {\text {K$\$$19743}}}{\sqrt [4]{\text {K$\$$19743}^2+1}}-\frac {2 a \sqrt [4]{\frac {\text {K$\$$19743}^2+1}{\text {K$\$$19743}^2}} \, _2F_1\left (\frac {1}{4},\frac {1}{2};\frac {3}{2};-\frac {1}{\text {K$\$$19743}^2}\right )}{\sqrt {\text {K$\$$19743}^2+1}}\right )\right \},\{y(x),\text {K$\$$19743}\}\right ],\text {Solve}\left [\left \{x=\frac {a^2 \text {K$\$$19743} y(\text {K$\$$19743})-\sqrt {a^2 \text {K$\$$19743}^2 \left (\text {K$\$$19743}^2+1\right ) y(\text {K$\$$19743})^4}}{a^2 \text {K$\$$19743}^2},y(x)=\frac {1}{4} \left (\frac {2 a \sqrt [4]{\frac {\text {K$\$$19743}^2+1}{\text {K$\$$19743}^2}} \, _2F_1\left (\frac {1}{4},\frac {1}{2};\frac {3}{2};-\frac {1}{\text {K$\$$19743}^2}\right )}{\sqrt {\text {K$\$$19743}^2+1}}-\frac {a c_1 \sqrt {\text {K$\$$19743}}}{\sqrt [4]{\text {K$\$$19743}^2+1}}\right )\right \},\{y(x),\text {K$\$$19743}\}\right ],\text {Solve}\left [\left \{x=\frac {\sqrt {a^2 \text {K$\$$22252}^2 \left (\text {K$\$$22252}^2+1\right ) y(\text {K$\$$22252})^4}+a^2 \text {K$\$$22252} y(\text {K$\$$22252})}{a^2 \text {K$\$$22252}^2},y(x)=\frac {1}{4} \left (\frac {a c_1 \sqrt {\text {K$\$$22252}}}{\sqrt [4]{\text {K$\$$22252}^2+1}}-\frac {2 a \sqrt [4]{\frac {\text {K$\$$22252}^2+1}{\text {K$\$$22252}^2}} \, _2F_1\left (\frac {1}{4},\frac {1}{2};\frac {3}{2};-\frac {1}{\text {K$\$$22252}^2}\right )}{\sqrt {\text {K$\$$22252}^2+1}}\right )\right \},\{y(x),\text {K$\$$22252}\}\right ],\text {Solve}\left [\left \{x=\frac {\sqrt {a^2 \text {K$\$$22252}^2 \left (\text {K$\$$22252}^2+1\right ) y(\text {K$\$$22252})^4}+a^2 \text {K$\$$22252} y(\text {K$\$$22252})}{a^2 \text {K$\$$22252}^2},y(x)=\frac {1}{4} \left (\frac {a c_1 \sqrt {\text {K$\$$22252}}}{\sqrt [4]{\text {K$\$$22252}^2+1}}+\frac {2 a \sqrt [4]{\frac {\text {K$\$$22252}^2+1}{\text {K$\$$22252}^2}} \, _2F_1\left (\frac {1}{4},\frac {1}{2};\frac {3}{2};-\frac {1}{\text {K$\$$22252}^2}\right )}{\sqrt {\text {K$\$$22252}^2+1}}\right )\right \},\{y(x),\text {K$\$$22252}\}\right ]\right \}\]
✗ Maple : cpu = 0. (sec), leaf count = 0 , exception
time expired