\[ \left (y(x)^4-a^2 x^2\right ) y'(x)^2+2 a^2 x y(x) y'(x)+y(x)^2 \left (y(x)^2-a^2\right )=0 \] ✓ Mathematica : cpu = 44.4174 (sec), leaf count = 395
DSolve[y[x]^2*(-a^2 + y[x]^2) + 2*a^2*x*y[x]*Derivative[1][y][x] + (-(a^2*x^2) + y[x]^4)*Derivative[1][y][x]^2 == 0,y[x],x]
\[\left \{\text {Solve}\left [\left \{x=\frac {a^2 K[1] y(K[1])-\sqrt {a^2 K[1]^2 \left (K[1]^2+1\right ) y(K[1])^4}}{a^2 K[1]^2},y(x)=\frac {-4 a \operatorname {Hypergeometric2F1}\left (-\frac {1}{4},\frac {1}{4},\frac {3}{4},-K[1]^2\right )-a c_1 \sqrt {K[1]}}{4 \sqrt [4]{K[1]^2+1}}\right \},\{y(x),K[1]\}\right ],\text {Solve}\left [\left \{x=\frac {a^2 K[1] y(K[1])-\sqrt {a^2 K[1]^2 \left (K[1]^2+1\right ) y(K[1])^4}}{a^2 K[1]^2},y(x)=\frac {4 a \operatorname {Hypergeometric2F1}\left (-\frac {1}{4},\frac {1}{4},\frac {3}{4},-K[1]^2\right )-a c_1 \sqrt {K[1]}}{4 \sqrt [4]{K[1]^2+1}}\right \},\{y(x),K[1]\}\right ],\text {Solve}\left [\left \{x=\frac {a^2 K[1] y(K[1])+\sqrt {a^2 K[1]^2 \left (K[1]^2+1\right ) y(K[1])^4}}{a^2 K[1]^2},y(x)=\frac {-4 a \operatorname {Hypergeometric2F1}\left (-\frac {1}{4},\frac {1}{4},\frac {3}{4},-K[1]^2\right )+a c_1 \sqrt {K[1]}}{4 \sqrt [4]{K[1]^2+1}}\right \},\{y(x),K[1]\}\right ],\text {Solve}\left [\left \{x=\frac {a^2 K[1] y(K[1])+\sqrt {a^2 K[1]^2 \left (K[1]^2+1\right ) y(K[1])^4}}{a^2 K[1]^2},y(x)=\frac {4 a \operatorname {Hypergeometric2F1}\left (-\frac {1}{4},\frac {1}{4},\frac {3}{4},-K[1]^2\right )+a c_1 \sqrt {K[1]}}{4 \sqrt [4]{K[1]^2+1}}\right \},\{y(x),K[1]\}\right ]\right \}\] ✓ Maple : cpu = 2.57 (sec), leaf count = 203
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))
\[y \left (x \right )-\operatorname {RootOf}\left (\textit {\_Z} \left (-\frac {a^{2} \left (2 \operatorname {RootOf}\left (\left (-y \left (x \right )^{4}+a^{2} x^{2}\right ) \textit {\_Z}^{2}+a^{2}-y \left (x \right )^{2}-2 \textit {\_Z} \,a^{2} x \right ) \textit {\_Z}^{2} x -\textit {\_Z}^{2}+x^{2}\right )}{\textit {\_Z}^{4}-a^{2} x^{2}}\right )^{\frac {1}{4}}+\sqrt {\operatorname {RootOf}\left (\left (-y \left (x \right )^{4}+a^{2} x^{2}\right ) \textit {\_Z}^{2}+a^{2}-y \left (x \right )^{2}-2 \textit {\_Z} \,a^{2} x \right ) \textit {\_Z}}\, c_{1}+a \operatorname {hypergeom}\left (\left [-\frac {1}{4}, \frac {1}{4}\right ], \left [\frac {3}{4}\right ], \frac {\textit {\_Z}^{2} \left (2 \operatorname {RootOf}\left (\left (-y \left (x \right )^{4}+a^{2} x^{2}\right ) \textit {\_Z}^{2}+a^{2}-y \left (x \right )^{2}-2 \textit {\_Z} \,a^{2} x \right ) a^{2} x +\textit {\_Z}^{2}-a^{2}\right )}{\textit {\_Z}^{4}-a^{2} x^{2}}\right )\right ) = 0\]