\[ f\left (x-\frac {3}{2} y'(x)^2\right )+y'(x)^3-y(x)=0 \] ✓ Mathematica : cpu = 0.015725 (sec), leaf count = 102
\[\left \{\left \{y(x)\to \frac {1}{9} \left (9 f\left (c_1\right )+2 \sqrt {6} x \sqrt {x-c_1}-2 \sqrt {6} c_1 \sqrt {x-c_1}\right ),y(x)\to \frac {1}{9} \left (9 f\left (c_1\right )-2 \sqrt {6} x \sqrt {x-c_1}+2 \sqrt {6} c_1 \sqrt {x-c_1}\right )\right \}\right \}\]
✓ Maple : cpu = 0.154 (sec), leaf count = 67
\[ \left \{ y \left ( x \right ) =f \left ( {\it \_C1} \right ) -{\frac {2}{9}\sqrt {-6\,{{\it \_C1}}^{3}+18\,{{\it \_C1}}^{2}x-18\,{\it \_C1}\,{x}^{2}+6\,{x}^{3}}},y \left ( x \right ) =f \left ( {\it \_C1} \right ) +{\frac {2}{9}\sqrt {-6\,{{\it \_C1}}^{3}+18\,{{\it \_C1}}^{2}x-18\,{\it \_C1}\,{x}^{2}+6\,{x}^{3}}} \right \} \]