\[ y''(x) \left (a \left (x y'(x)-y(x)\right )+y'(x)^2\right )-b=0 \] ✗ Mathematica : cpu = 0.177073 (sec), leaf count = 0 , could not solve
DSolve[-b + (Derivative[1][y][x]^2 + a*(-y[x] + x*Derivative[1][y][x]))*Derivative[2][y][x] == 0, y[x], x]
✓ Maple : cpu = 0.446 (sec), leaf count = 289
\[ \left \{ y \left ( x \right ) =-{\frac {a{x}^{2}}{4}}+{\it RootOf} \left ( -x-\int ^{{\it \_Z}}\!{\frac {1}{{a}^{2}{{\it \_f}}^{2}-4\,{\it \_f}\,b+2\,{\it \_C1}}\sqrt { \left ( {a}^{2}{{\it \_f}}^{2}-4\,{\it \_f}\,b+2\,{\it \_C1} \right ) \left ( a{\it \_f}+\sqrt {4\,{\it \_f}\,b-2\,{\it \_C1}} \right ) }}{d{\it \_f}}+{\it \_C2} \right ) ,y \left ( x \right ) =-{\frac {a{x}^{2}}{4}}+{\it RootOf} \left ( -x+\int ^{{\it \_Z}}\!{\frac {1}{{a}^{2}{{\it \_f}}^{2}-4\,{\it \_f}\,b+2\,{\it \_C1}}\sqrt { \left ( {a}^{2}{{\it \_f}}^{2}-4\,{\it \_f}\,b+2\,{\it \_C1} \right ) \left ( a{\it \_f}+\sqrt {4\,{\it \_f}\,b-2\,{\it \_C1}} \right ) }}{d{\it \_f}}+{\it \_C2} \right ) ,y \left ( x \right ) =-{\frac {a{x}^{2}}{4}}+{\it RootOf} \left ( -x-\int ^{{\it \_Z}}\!{\frac {1}{{a}^{2}{{\it \_f}}^{2}-4\,{\it \_f}\,b+2\,{\it \_C1}}\sqrt {- \left ( {a}^{2}{{\it \_f}}^{2}-4\,{\it \_f}\,b+2\,{\it \_C1} \right ) \left ( -a{\it \_f}+\sqrt {4\,{\it \_f}\,b-2\,{\it \_C1}} \right ) }}{d{\it \_f}}+{\it \_C2} \right ) ,y \left ( x \right ) =-{\frac {a{x}^{2}}{4}}+{\it RootOf} \left ( -x+\int ^{{\it \_Z}}\!{\frac {1}{{a}^{2}{{\it \_f}}^{2}-4\,{\it \_f}\,b+2\,{\it \_C1}}\sqrt {- \left ( {a}^{2}{{\it \_f}}^{2}-4\,{\it \_f}\,b+2\,{\it \_C1} \right ) \left ( -a{\it \_f}+\sqrt {4\,{\it \_f}\,b-2\,{\it \_C1}} \right ) }}{d{\it \_f}}+{\it \_C2} \right ) \right \} \]