\[ \boxed { \left ( \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}+a \left ( x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -y \left ( x \right ) \right ) \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) -b=0} \]
Mathematica: cpu = 0.170022 (sec), leaf count = 35 \[ \text {DSolve}\left [y''(x) \left (a \left (x y'(x)-y(x)\right )+y'(x)^2\right )-b=0,y(x),x\right ] \]
Maple: cpu = 0.281 (sec), leaf count = 423 \[ \left \{ y \left ( x \right ) =-{\frac {a{x}^{2}}{4}}+{\it RootOf} \left ( -x-\int ^{{\it \_Z}}\!{\frac {1}{{{\it \_f}}^{2}{a}^{2}-4\,{ \it \_f}\,b+2\,{\it \_C1}}\sqrt {{{\it \_f}}^{3}{a}^{3}-4\,a{{\it \_f} }^{2}b+2\,a{\it \_f}\,{\it \_C1}-\sqrt {4\,{\it \_f}\,b-2\,{\it \_C1}} {{\it \_f}}^{2}{a}^{2}+4\,\sqrt {4\,{\it \_f}\,b-2\,{\it \_C1}}b{\it \_f}-2\,\sqrt {4\,{\it \_f}\,b-2\,{\it \_C1}}{\it \_C1}}}{d{\it \_f}}+ {\it \_C2} \right ) ,y \left ( x \right ) =-{\frac {a{x}^{2}}{4}}+{\it RootOf} \left ( -x+\int ^{{\it \_Z}}\!{\frac {1}{{{\it \_f}}^{2}{a}^{2} -4\,{\it \_f}\,b+2\,{\it \_C1}}\sqrt {{{\it \_f}}^{3}{a}^{3}-4\,a{{ \it \_f}}^{2}b+2\,a{\it \_f}\,{\it \_C1}-\sqrt {4\,{\it \_f}\,b-2\,{ \it \_C1}}{{\it \_f}}^{2}{a}^{2}+4\,\sqrt {4\,{\it \_f}\,b-2\,{\it \_C1}}b{\it \_f}-2\,\sqrt {4\,{\it \_f}\,b-2\,{\it \_C1}}{\it \_C1}}}{ d{\it \_f}}+{\it \_C2} \right ) ,y \left ( x \right ) =-{\frac {a{x}^{2} }{4}}+{\it RootOf} \left ( -x-\int ^{{\it \_Z}}\!{\frac {1}{{{\it \_f}} ^{2}{a}^{2}-4\,{\it \_f}\,b+2\,{\it \_C1}}\sqrt {{{\it \_f}}^{3}{a}^{3 }-4\,a{{\it \_f}}^{2}b+2\,a{\it \_f}\,{\it \_C1}+\sqrt {4\,{\it \_f}\, b-2\,{\it \_C1}}{{\it \_f}}^{2}{a}^{2}-4\,\sqrt {4\,{\it \_f}\,b-2\,{ \it \_C1}}b{\it \_f}+2\,\sqrt {4\,{\it \_f}\,b-2\,{\it \_C1}}{\it \_C1 }}}{d{\it \_f}}+{\it \_C2} \right ) ,y \left ( x \right ) =-{\frac {a{x}^ {2}}{4}}+{\it RootOf} \left ( -x+\int ^{{\it \_Z}}\!{\frac {1}{{{\it \_f}}^{2}{a}^{2}-4\,{\it \_f}\,b+2\,{\it \_C1}}\sqrt {{{\it \_f}}^{3}{ a}^{3}-4\,a{{\it \_f}}^{2}b+2\,a{\it \_f}\,{\it \_C1}+\sqrt {4\,{\it \_f}\,b-2\,{\it \_C1}}{{\it \_f}}^{2}{a}^{2}-4\,\sqrt {4\,{\it \_f}\,b -2\,{\it \_C1}}b{\it \_f}+2\,\sqrt {4\,{\it \_f}\,b-2\,{\it \_C1}}{ \it \_C1}}}{d{\it \_f}}+{\it \_C2} \right ) \right \} \]