\[ a^2 \left (-x^2\right )-2 a^2 x y(x) y'(x)+\left (1-a^2\right ) y(x)^2 y'(x)^2+y(x)^2=0 \] ✓ Mathematica : cpu = 0.366741 (sec), leaf count = 212
DSolve[-(a^2*x^2) + y[x]^2 - 2*a^2*x*y[x]*Derivative[1][y][x] + (1 - a^2)*y[x]^2*Derivative[1][y][x]^2 == 0,y[x],x]
\[\left \{\left \{y(x)\to -\frac {\sqrt {a^6 \left (-x^2\right )+3 a^4 x^2-3 a^2 x^2+2 a^2 x e^{a^2 c_1-c_1}-2 x e^{a^2 c_1-c_1}+e^{2 a^2 c_1-2 c_1}+x^2}}{\sqrt {a^6-3 a^4+3 a^2-1}}\right \},\left \{y(x)\to \frac {\sqrt {a^6 \left (-x^2\right )+3 a^4 x^2-3 a^2 x^2+2 a^2 x e^{a^2 c_1-c_1}-2 x e^{a^2 c_1-c_1}+e^{2 a^2 c_1-2 c_1}+x^2}}{\sqrt {a^6-3 a^4+3 a^2-1}}\right \}\right \}\] ✓ Maple : cpu = 0.211 (sec), leaf count = 189
dsolve((-a^2+1)*y(x)^2*diff(y(x),x)^2-2*a^2*x*y(x)*diff(y(x),x)+y(x)^2-a^2*x^2 = 0,y(x))
\[y \left (x \right ) = \frac {x a}{\sqrt {-a^{2}+1}}\]