\[ f\left (x-\frac {3}{2} y'(x)^2\right )+y'(x)^3-y(x)=0 \] ✓ Mathematica : cpu = 0.0339602 (sec), leaf count = 102
\[\left \{\left \{y(x)\to \frac {1}{9} \left (9 f(c_1)+2 \sqrt {6} x \sqrt {x-c_1}-2 \sqrt {6} c_1 \sqrt {x-c_1}\right ),y(x)\to \frac {1}{9} \left (9 f(c_1)-2 \sqrt {6} x \sqrt {x-c_1}+2 \sqrt {6} c_1 \sqrt {x-c_1}\right )\right \}\right \}\] ✓ Maple : cpu = 0.141 (sec), leaf count = 41
\[y \relax (x ) = f \left (c_{1}\right )-\frac {2 \sqrt {6}\, \sqrt {\left (-c_{1}+x \right )^{3}}}{9}\]