\[ \left (y(x)^4-a^2 x^2\right ) y'(x)^2+2 a^2 x y(x) y'(x)+y(x)^2 \left (y(x)^2-a^2\right )=0 \] ✓ Mathematica : cpu = 30.9609 (sec), leaf count = 408
\[\left \{\text {Solve}\left [\left \{x=\frac {\text {K$\$$3275690} y(\text {K$\$$3275690})-\frac {\sqrt {a^2 \left (\text {K$\$$3275690}^4+\text {K$\$$3275690}^2\right ) y(\text {K$\$$3275690})^4}}{a^2}}{\text {K$\$$3275690}^2},a c_1 \sqrt {\text {K$\$$3275690}}+\frac {2 a \sqrt [4]{\frac {1}{\text {K$\$$3275690}^2}+1} \, _2F_1\left (\frac {1}{4},\frac {1}{2};\frac {3}{2};-\frac {1}{\text {K$\$$3275690}^2}\right )}{\sqrt [4]{\text {K$\$$3275690}^2+1}}+4 \sqrt [4]{\text {K$\$$3275690}^2+1} y(x)=0\right \},\{y(x),\text {K$\$$3275690}\}\right ],\text {Solve}\left [\left \{x=\frac {\text {K$\$$3275690} y(\text {K$\$$3275690})-\frac {\sqrt {a^2 \left (\text {K$\$$3275690}^4+\text {K$\$$3275690}^2\right ) y(\text {K$\$$3275690})^4}}{a^2}}{\text {K$\$$3275690}^2},a c_1 \sqrt {\text {K$\$$3275690}}+4 \sqrt [4]{\text {K$\$$3275690}^2+1} y(x)=\frac {2 a \sqrt [4]{\frac {1}{\text {K$\$$3275690}^2}+1} \, _2F_1\left (\frac {1}{4},\frac {1}{2};\frac {3}{2};-\frac {1}{\text {K$\$$3275690}^2}\right )}{\sqrt [4]{\text {K$\$$3275690}^2+1}}\right \},\{y(x),\text {K$\$$3275690}\}\right ],\text {Solve}\left [\left \{x=\frac {\sqrt {a^2 \left (\text {K$\$$3278196}^4+\text {K$\$$3278196}^2\right ) y(\text {K$\$$3278196})^4}+a^2 \text {K$\$$3278196} y(\text {K$\$$3278196})}{a^2 \text {K$\$$3278196}^2},\frac {2 a \sqrt [4]{\frac {1}{\text {K$\$$3278196}^2}+1} \, _2F_1\left (\frac {1}{4},\frac {1}{2};\frac {3}{2};-\frac {1}{\text {K$\$$3278196}^2}\right )}{\sqrt [4]{\text {K$\$$3278196}^2+1}}+4 \sqrt [4]{\text {K$\$$3278196}^2+1} y(x)=a c_1 \sqrt {\text {K$\$$3278196}}\right \},\{y(x),\text {K$\$$3278196}\}\right ],\text {Solve}\left [\left \{x=\frac {\sqrt {a^2 \left (\text {K$\$$3278196}^4+\text {K$\$$3278196}^2\right ) y(\text {K$\$$3278196})^4}+a^2 \text {K$\$$3278196} y(\text {K$\$$3278196})}{a^2 \text {K$\$$3278196}^2},4 \sqrt [4]{\text {K$\$$3278196}^2+1} y(x)=a c_1 \sqrt {\text {K$\$$3278196}}+\frac {2 a \sqrt [4]{\frac {1}{\text {K$\$$3278196}^2}+1} \, _2F_1\left (\frac {1}{4},\frac {1}{2};\frac {3}{2};-\frac {1}{\text {K$\$$3278196}^2}\right )}{\sqrt [4]{\text {K$\$$3278196}^2+1}}\right \},\{y(x),\text {K$\$$3278196}\}\right ]\right \}\]
✗ Maple : cpu = 0. (sec), leaf count = 0 , exception
time expired