\[ y''(x) \left (a \left (x y'(x)-y(x)\right )+y'(x)^2\right )-b=0 \] ✗ Mathematica : cpu = 0.202637 (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 = 0.416 (sec), leaf count = 423
\[ \left \{ y \left ( x \right ) =-{\frac {a{x}^{2}}{4}}+{\it RootOf} \left ( -x-\int ^{{\it \_Z}}\!{\frac {1}{{{\it \_f}}^{2}{a}^{2}-4\,{\it \_f}\,b+2\,{\it \_C1}}\sqrt {{{\it \_f}}^{3}{a}^{3}-4\,a{{\it \_f}}^{2}b+2\,a{\it \_f}\,{\it \_C1}-\sqrt {4\,{\it \_f}\,b-2\,{\it \_C1}}{{\it \_f}}^{2}{a}^{2}+4\,\sqrt {4\,{\it \_f}\,b-2\,{\it \_C1}}b{\it \_f}-2\,\sqrt {4\,{\it \_f}\,b-2\,{\it \_C1}}{\it \_C1}}}{d{\it \_f}}+{\it \_C2} \right ) ,y \left ( x \right ) =-{\frac {a{x}^{2}}{4}}+{\it RootOf} \left ( -x+\int ^{{\it \_Z}}\!{\frac {1}{{{\it \_f}}^{2}{a}^{2}-4\,{\it \_f}\,b+2\,{\it \_C1}}\sqrt {{{\it \_f}}^{3}{a}^{3}-4\,a{{\it \_f}}^{2}b+2\,a{\it \_f}\,{\it \_C1}-\sqrt {4\,{\it \_f}\,b-2\,{\it \_C1}}{{\it \_f}}^{2}{a}^{2}+4\,\sqrt {4\,{\it \_f}\,b-2\,{\it \_C1}}b{\it \_f}-2\,\sqrt {4\,{\it \_f}\,b-2\,{\it \_C1}}{\it \_C1}}}{d{\it \_f}}+{\it \_C2} \right ) ,y \left ( x \right ) =-{\frac {a{x}^{2}}{4}}+{\it RootOf} \left ( -x-\int ^{{\it \_Z}}\!{\frac {1}{{{\it \_f}}^{2}{a}^{2}-4\,{\it \_f}\,b+2\,{\it \_C1}}\sqrt {{{\it \_f}}^{3}{a}^{3}-4\,a{{\it \_f}}^{2}b+2\,a{\it \_f}\,{\it \_C1}+\sqrt {4\,{\it \_f}\,b-2\,{\it \_C1}}{{\it \_f}}^{2}{a}^{2}-4\,\sqrt {4\,{\it \_f}\,b-2\,{\it \_C1}}b{\it \_f}+2\,\sqrt {4\,{\it \_f}\,b-2\,{\it \_C1}}{\it \_C1}}}{d{\it \_f}}+{\it \_C2} \right ) ,y \left ( x \right ) =-{\frac {a{x}^{2}}{4}}+{\it RootOf} \left ( -x+\int ^{{\it \_Z}}\!{\frac {1}{{{\it \_f}}^{2}{a}^{2}-4\,{\it \_f}\,b+2\,{\it \_C1}}\sqrt {{{\it \_f}}^{3}{a}^{3}-4\,a{{\it \_f}}^{2}b+2\,a{\it \_f}\,{\it \_C1}+\sqrt {4\,{\it \_f}\,b-2\,{\it \_C1}}{{\it \_f}}^{2}{a}^{2}-4\,\sqrt {4\,{\it \_f}\,b-2\,{\it \_C1}}b{\it \_f}+2\,\sqrt {4\,{\it \_f}\,b-2\,{\it \_C1}}{\it \_C1}}}{d{\it \_f}}+{\it \_C2} \right ) \right \} \]