\[ \left (x y'(x)-y(x)\right ) \left (a x^2+b x+c\right )+x^2-y(x)^2=0 \] ✓ Mathematica : cpu = 0.372908 (sec), leaf count = 132
DSolve[x^2 - y[x]^2 + (c + b*x + a*x^2)*(-y[x] + x*Derivative[1][y][x]) == 0,y[x],x]
\[\left \{\left \{y(x)\to -\frac {x \left (-1+\exp \left (\frac {4 \tan ^{-1}\left (\frac {2 a x}{\sqrt {4 a c-b^2}}+\frac {b}{\sqrt {4 a c-b^2}}\right )}{\sqrt {4 a c-b^2}}+2 c_1\right )\right )}{1+\exp \left (\frac {4 \tan ^{-1}\left (\frac {2 a x}{\sqrt {4 a c-b^2}}+\frac {b}{\sqrt {4 a c-b^2}}\right )}{\sqrt {4 a c-b^2}}+2 c_1\right )}\right \}\right \}\] ✓ Maple : cpu = 0.064 (sec), leaf count = 58
dsolve((a*x^2+b*x+c)*(x*diff(y(x),x)-y(x))-y(x)^2+x^2 = 0,y(x))
\[y \left (x \right ) = -\tanh \left (\frac {c_{1} \sqrt {4 a c -b^{2}}+2 \arctan \left (\frac {2 a x +b}{\sqrt {4 a c -b^{2}}}\right )}{\sqrt {4 a c -b^{2}}}\right ) x\]