\[ \left (y(x)^4-a^2 x^2\right ) y'(x)^2+2 a^2 x y(x) y'(x)+y(x)^2 \left (y(x)^2-a^2\right )=0 \] ✓ Mathematica : cpu = 32.6985 (sec), leaf count = 408
\[\left \{\text {Solve}\left [\left \{x=\frac {\text {K$\$$3073764} y(\text {K$\$$3073764})-\frac {\sqrt {a^2 \left (\text {K$\$$3073764}^4+\text {K$\$$3073764}^2\right ) y(\text {K$\$$3073764})^4}}{a^2}}{\text {K$\$$3073764}^2},a c_1 \sqrt {\text {K$\$$3073764}}+\frac {2 a \sqrt [4]{\frac {1}{\text {K$\$$3073764}^2}+1} \, _2F_1\left (\frac {1}{4},\frac {1}{2};\frac {3}{2};-\frac {1}{\text {K$\$$3073764}^2}\right )}{\sqrt [4]{\text {K$\$$3073764}^2+1}}+4 \sqrt [4]{\text {K$\$$3073764}^2+1} y(x)=0\right \},\{y(x),\text {K$\$$3073764}\}\right ],\text {Solve}\left [\left \{x=\frac {\text {K$\$$3073764} y(\text {K$\$$3073764})-\frac {\sqrt {a^2 \left (\text {K$\$$3073764}^4+\text {K$\$$3073764}^2\right ) y(\text {K$\$$3073764})^4}}{a^2}}{\text {K$\$$3073764}^2},a c_1 \sqrt {\text {K$\$$3073764}}+4 \sqrt [4]{\text {K$\$$3073764}^2+1} y(x)=\frac {2 a \sqrt [4]{\frac {1}{\text {K$\$$3073764}^2}+1} \, _2F_1\left (\frac {1}{4},\frac {1}{2};\frac {3}{2};-\frac {1}{\text {K$\$$3073764}^2}\right )}{\sqrt [4]{\text {K$\$$3073764}^2+1}}\right \},\{y(x),\text {K$\$$3073764}\}\right ],\text {Solve}\left [\left \{x=\frac {\sqrt {a^2 \left (\text {K$\$$3076270}^4+\text {K$\$$3076270}^2\right ) y(\text {K$\$$3076270})^4}+a^2 \text {K$\$$3076270} y(\text {K$\$$3076270})}{a^2 \text {K$\$$3076270}^2},\frac {2 a \sqrt [4]{\frac {1}{\text {K$\$$3076270}^2}+1} \, _2F_1\left (\frac {1}{4},\frac {1}{2};\frac {3}{2};-\frac {1}{\text {K$\$$3076270}^2}\right )}{\sqrt [4]{\text {K$\$$3076270}^2+1}}+4 \sqrt [4]{\text {K$\$$3076270}^2+1} y(x)=a c_1 \sqrt {\text {K$\$$3076270}}\right \},\{y(x),\text {K$\$$3076270}\}\right ],\text {Solve}\left [\left \{x=\frac {\sqrt {a^2 \left (\text {K$\$$3076270}^4+\text {K$\$$3076270}^2\right ) y(\text {K$\$$3076270})^4}+a^2 \text {K$\$$3076270} y(\text {K$\$$3076270})}{a^2 \text {K$\$$3076270}^2},4 \sqrt [4]{\text {K$\$$3076270}^2+1} y(x)=a c_1 \sqrt {\text {K$\$$3076270}}+\frac {2 a \sqrt [4]{\frac {1}{\text {K$\$$3076270}^2}+1} \, _2F_1\left (\frac {1}{4},\frac {1}{2};\frac {3}{2};-\frac {1}{\text {K$\$$3076270}^2}\right )}{\sqrt [4]{\text {K$\$$3076270}^2+1}}\right \},\{y(x),\text {K$\$$3076270}\}\right ]\right \}\]
✗ Maple : cpu = 0. (sec), leaf count = 0 , exception
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