\[ \left (y(x)^4-a^2 x^2\right ) y'(x)^2+2 a^2 x y(x) y'(x)+y(x)^2 \left (y(x)^2-a^2\right )=0 \] ✓ Mathematica : cpu = 30.8191 (sec), leaf count = 443
\[\left \{\text {Solve}\left [\left \{x=\frac {a^2 \text {K$\$$12637961} y(\text {K$\$$12637961})-\sqrt {a^2 \text {K$\$$12637961}^2 \left (\text {K$\$$12637961}^2+1\right ) y(\text {K$\$$12637961})^4}}{a^2 \text {K$\$$12637961}^2},y(x)=\frac {1}{4} \left (-\frac {a c_1 \sqrt {\text {K$\$$12637961}}}{\sqrt [4]{\text {K$\$$12637961}^2+1}}-\frac {2 a \sqrt [4]{\frac {\text {K$\$$12637961}^2+1}{\text {K$\$$12637961}^2}} \, _2F_1\left (\frac {1}{4},\frac {1}{2};\frac {3}{2};-\frac {1}{\text {K$\$$12637961}^2}\right )}{\sqrt {\text {K$\$$12637961}^2+1}}\right )\right \},\{y(x),\text {K$\$$12637961}\}\right ],\text {Solve}\left [\left \{x=\frac {a^2 \text {K$\$$12637961} y(\text {K$\$$12637961})-\sqrt {a^2 \text {K$\$$12637961}^2 \left (\text {K$\$$12637961}^2+1\right ) y(\text {K$\$$12637961})^4}}{a^2 \text {K$\$$12637961}^2},y(x)=\frac {1}{4} \left (\frac {2 a \sqrt [4]{\frac {\text {K$\$$12637961}^2+1}{\text {K$\$$12637961}^2}} \, _2F_1\left (\frac {1}{4},\frac {1}{2};\frac {3}{2};-\frac {1}{\text {K$\$$12637961}^2}\right )}{\sqrt {\text {K$\$$12637961}^2+1}}-\frac {a c_1 \sqrt {\text {K$\$$12637961}}}{\sqrt [4]{\text {K$\$$12637961}^2+1}}\right )\right \},\{y(x),\text {K$\$$12637961}\}\right ],\text {Solve}\left [\left \{x=\frac {\sqrt {a^2 \text {K$\$$12640467}^2 \left (\text {K$\$$12640467}^2+1\right ) y(\text {K$\$$12640467})^4}+a^2 \text {K$\$$12640467} y(\text {K$\$$12640467})}{a^2 \text {K$\$$12640467}^2},y(x)=\frac {1}{4} \left (\frac {a c_1 \sqrt {\text {K$\$$12640467}}}{\sqrt [4]{\text {K$\$$12640467}^2+1}}-\frac {2 a \sqrt [4]{\frac {\text {K$\$$12640467}^2+1}{\text {K$\$$12640467}^2}} \, _2F_1\left (\frac {1}{4},\frac {1}{2};\frac {3}{2};-\frac {1}{\text {K$\$$12640467}^2}\right )}{\sqrt {\text {K$\$$12640467}^2+1}}\right )\right \},\{y(x),\text {K$\$$12640467}\}\right ],\text {Solve}\left [\left \{x=\frac {\sqrt {a^2 \text {K$\$$12640467}^2 \left (\text {K$\$$12640467}^2+1\right ) y(\text {K$\$$12640467})^4}+a^2 \text {K$\$$12640467} y(\text {K$\$$12640467})}{a^2 \text {K$\$$12640467}^2},y(x)=\frac {1}{4} \left (\frac {a c_1 \sqrt {\text {K$\$$12640467}}}{\sqrt [4]{\text {K$\$$12640467}^2+1}}+\frac {2 a \sqrt [4]{\frac {\text {K$\$$12640467}^2+1}{\text {K$\$$12640467}^2}} \, _2F_1\left (\frac {1}{4},\frac {1}{2};\frac {3}{2};-\frac {1}{\text {K$\$$12640467}^2}\right )}{\sqrt {\text {K$\$$12640467}^2+1}}\right )\right \},\{y(x),\text {K$\$$12640467}\}\right ]\right \}\] ✗ Maple : cpu = 0. (sec), leaf count = 0 , could not solve
dsolve((y(x)^4-a^2*x^2)*diff(y(x),x)^2+2*a^2*x*y(x)*diff(y(x),x)+y(x)^2*(y(x)^2-a^2)=0,y(x))