\[ a \left (x y'(x)-y(x)\right )^2-b+x y''(x)=0 \] ✓ Mathematica : cpu = 6.76141 (sec), leaf count = 51
DSolve[-b + a*(-y[x] + x*Derivative[1][y][x])^2 + x*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to x \left (\int _1^x\frac {\sqrt {-\frac {b}{a}} \tan \left (c_1-a \sqrt {-\frac {b}{a}} K[2]\right )}{K[2]^2}dK[2]+c_2\right )\right \}\right \}\] ✓ Maple : cpu = 1.332 (sec), leaf count = 35
dsolve(x*diff(diff(y(x),x),x)+a*(x*diff(y(x),x)-y(x))^2-b=0,y(x))
\[y \left (x \right ) = \left (\int \frac {i \tan \left (-i \sqrt {a}\, \sqrt {b}\, x +c_{1}\right ) \sqrt {b}}{\sqrt {a}\, x^{2}}d x +c_{2}\right ) x\]