\[ -a x y(x) y'(x)+2 a y(x)^2+y'(x)^2=0 \] ✓ Mathematica : cpu = 0.0806359 (sec), leaf count = 135
DSolve[2*a*y[x]^2 - a*x*y[x]*Derivative[1][y][x] + Derivative[1][y][x]^2 == 0,y[x],x]
\[\left \{\left \{y(x)\to c_1 \exp \left (\frac {1}{2} \left (\frac {a x^2}{2}+\frac {1}{2} \sqrt {a} x \sqrt {a x^2-8}-4 \log \left (\sqrt {a} \sqrt {a x^2-8}+a x\right )\right )\right )\right \},\left \{y(x)\to c_1 \exp \left (\frac {1}{2} \left (\frac {a x^2}{2}-\frac {1}{2} \sqrt {a} x \sqrt {a x^2-8}+4 \log \left (\sqrt {a} \sqrt {a x^2-8}+a x\right )\right )\right )\right \}\right \}\] ✓ Maple : cpu = 0.075 (sec), leaf count = 122
dsolve(diff(y(x),x)^2-a*x*y(x)*diff(y(x),x)+2*a*y(x)^2=0,y(x))
\[y \left (x \right ) = c_{1} \left (\frac {a^{2} x}{\sqrt {a^{2}}}+\sqrt {a^{2} x^{2}-8 a}\right )^{-\frac {2 a}{\sqrt {a^{2}}}} {\mathrm e}^{\frac {x \left (a x +\sqrt {a^{2} x^{2}-8 a}\right )}{4}}\]