\[ a x^2+2 x y(x) y'(x)-y(x)^2=0 \] ✓ Mathematica : cpu = 0.0967095 (sec), leaf count = 41
DSolve[a*x^2 - y[x]^2 + 2*x*y[x]*Derivative[1][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to -\sqrt {-a x^2+c_1 x}\right \},\left \{y(x)\to \sqrt {-a x^2+c_1 x}\right \}\right \}\] ✓ Maple : cpu = 0.018 (sec), leaf count = 33
dsolve(2*x*y(x)*diff(y(x),x)-y(x)^2+a*x^2 = 0,y(x))
\[y \left (x \right ) = \sqrt {-a \,x^{2}+c_{1} x}\]