\[ x^2 \left (x^2-a^2\right ) y'(x)^2-1=0 \] ✓ Mathematica : cpu = 0.0212745 (sec), leaf count = 120
DSolve[-1 + x^2*(-a^2 + x^2)*Derivative[1][y][x]^2 == 0,y[x],x]
\[\left \{\left \{y(x)\to -\frac {x \sqrt {x^2-a^2} \tan ^{-1}\left (\frac {\sqrt {x^2-a^2}}{a}\right )}{a \sqrt {x^4-a^2 x^2}}+c_1\right \},\left \{y(x)\to \frac {x \sqrt {x^2-a^2} \tan ^{-1}\left (\frac {\sqrt {x^2-a^2}}{a}\right )}{a \sqrt {x^4-a^2 x^2}}+c_1\right \}\right \}\] ✓ Maple : cpu = 0.058 (sec), leaf count = 90
dsolve(x^2*(-a^2+x^2)*diff(y(x),x)^2-1 = 0,y(x))
\[y \left (x \right ) = -\frac {\ln \left (\frac {-2 a^{2}+2 \sqrt {-a^{2}}\, \sqrt {-a^{2}+x^{2}}}{x}\right )}{\sqrt {-a^{2}}}+c_{1}\]