\[ \left (y(x)^4-a^2 x^2\right ) y'(x)^2+2 a^2 x y(x) y'(x)+y(x)^2 \left (y(x)^2-a^2\right )=0 \] ✓ Mathematica : cpu = 32.4331 (sec), leaf count = 408
\[\left \{\text {Solve}\left [\left \{x=\frac {\text {K$\$$931688} y(\text {K$\$$931688})-\frac {\sqrt {a^2 \left (\text {K$\$$931688}^4+\text {K$\$$931688}^2\right ) y(\text {K$\$$931688})^4}}{a^2}}{\text {K$\$$931688}^2},a c_1 \sqrt {\text {K$\$$931688}}+\frac {2 a \sqrt [4]{\frac {1}{\text {K$\$$931688}^2}+1} \, _2F_1\left (\frac {1}{4},\frac {1}{2};\frac {3}{2};-\frac {1}{\text {K$\$$931688}^2}\right )}{\sqrt [4]{\text {K$\$$931688}^2+1}}+4 \sqrt [4]{\text {K$\$$931688}^2+1} y(x)=0\right \},\{y(x),\text {K$\$$931688}\}\right ],\text {Solve}\left [\left \{x=\frac {\text {K$\$$931688} y(\text {K$\$$931688})-\frac {\sqrt {a^2 \left (\text {K$\$$931688}^4+\text {K$\$$931688}^2\right ) y(\text {K$\$$931688})^4}}{a^2}}{\text {K$\$$931688}^2},a c_1 \sqrt {\text {K$\$$931688}}+4 \sqrt [4]{\text {K$\$$931688}^2+1} y(x)=\frac {2 a \sqrt [4]{\frac {1}{\text {K$\$$931688}^2}+1} \, _2F_1\left (\frac {1}{4},\frac {1}{2};\frac {3}{2};-\frac {1}{\text {K$\$$931688}^2}\right )}{\sqrt [4]{\text {K$\$$931688}^2+1}}\right \},\{y(x),\text {K$\$$931688}\}\right ],\text {Solve}\left [\left \{x=\frac {\sqrt {a^2 \left (\text {K$\$$934189}^4+\text {K$\$$934189}^2\right ) y(\text {K$\$$934189})^4}+a^2 \text {K$\$$934189} y(\text {K$\$$934189})}{a^2 \text {K$\$$934189}^2},\frac {2 a \sqrt [4]{\frac {1}{\text {K$\$$934189}^2}+1} \, _2F_1\left (\frac {1}{4},\frac {1}{2};\frac {3}{2};-\frac {1}{\text {K$\$$934189}^2}\right )}{\sqrt [4]{\text {K$\$$934189}^2+1}}+4 \sqrt [4]{\text {K$\$$934189}^2+1} y(x)=a c_1 \sqrt {\text {K$\$$934189}}\right \},\{y(x),\text {K$\$$934189}\}\right ],\text {Solve}\left [\left \{x=\frac {\sqrt {a^2 \left (\text {K$\$$934189}^4+\text {K$\$$934189}^2\right ) y(\text {K$\$$934189})^4}+a^2 \text {K$\$$934189} y(\text {K$\$$934189})}{a^2 \text {K$\$$934189}^2},4 \sqrt [4]{\text {K$\$$934189}^2+1} y(x)=a c_1 \sqrt {\text {K$\$$934189}}+\frac {2 a \sqrt [4]{\frac {1}{\text {K$\$$934189}^2}+1} \, _2F_1\left (\frac {1}{4},\frac {1}{2};\frac {3}{2};-\frac {1}{\text {K$\$$934189}^2}\right )}{\sqrt [4]{\text {K$\$$934189}^2+1}}\right \},\{y(x),\text {K$\$$934189}\}\right ]\right \}\]
✗ Maple : cpu = 0. (sec), leaf count = 0 , exception
time expired