\[ y''(x) \left (a \left (x y'(x)-y(x)\right )+y'(x)^2\right )-b=0 \] ✓ Mathematica : cpu = 0.265547 (sec), leaf count = 281
DSolve[-b + (Derivative[1][y][x]^2 + a*(-y[x] + x*Derivative[1][y][x]))*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\text {Solve}\left [-\int \frac {a \left (\frac {a x^2}{4}+y(x)\right )+\sqrt {4 b \left (\frac {a x^2}{4}+y(x)\right )-2 c_1}}{\sqrt {\left (a^2 \left (\frac {a x^2}{4}+y(x)\right )^2-4 b \left (\frac {a x^2}{4}+y(x)\right )+2 c_1\right ) \left (a \left (\frac {a x^2}{4}+y(x)\right )+\sqrt {4 b \left (\frac {a x^2}{4}+y(x)\right )-2 c_1}\right )}}d\left (\frac {a x^2}{4}+y(x)\right )=-x+c_2,y(x)\right ],\text {Solve}\left [\int \frac {a \left (\frac {a x^2}{4}+y(x)\right )+\sqrt {4 b \left (\frac {a x^2}{4}+y(x)\right )-2 c_1}}{\sqrt {\left (a^2 \left (\frac {a x^2}{4}+y(x)\right )^2-4 b \left (\frac {a x^2}{4}+y(x)\right )+2 c_1\right ) \left (a \left (\frac {a x^2}{4}+y(x)\right )+\sqrt {4 b \left (\frac {a x^2}{4}+y(x)\right )-2 c_1}\right )}}d\left (\frac {a x^2}{4}+y(x)\right )=-x+c_2,y(x)\right ]\right \}\] ✓ Maple : cpu = 0.458 (sec), leaf count = 289
dsolve((diff(y(x),x)^2+a*(x*diff(y(x),x)-y(x)))*diff(diff(y(x),x),x)-b=0,y(x))
\[y \left (x \right ) = -\frac {a \,x^{2}}{4}+\RootOf \left (-x +\int _{}^{\textit {\_Z}}\frac {\sqrt {\left (\textit {\_f}^{2} a^{2}-4 \textit {\_f} b +2 c_{1}\right ) \left (\textit {\_f} a +\sqrt {4 \textit {\_f} b -2 c_{1}}\right )}}{\textit {\_f}^{2} a^{2}-4 \textit {\_f} b +2 c_{1}}d \textit {\_f} +c_{2}\right )\]