\[ f\left (x-\frac {3}{2} y'(x)^2\right )+y'(x)^3-y(x)=0 \] ✓ Mathematica : cpu = 0.0161279 (sec), leaf count = 62
\[\left \{\left \{y(x)\to \frac {1}{9} \left (9 f\left (c_1\right )+2 \sqrt {6} \left (x-c_1\right ){}^{3/2}\right ),y(x)\to \frac {1}{9} \left (9 f\left (c_1\right )-2 \sqrt {6} \left (x-c_1\right ){}^{3/2}\right )\right \}\right \}\]
✓ Maple : cpu = 0.508 (sec), leaf count = 41
\[ \left \{ y \left ( x \right ) =f \left ( {\it \_C1} \right ) -{\frac {2\,\sqrt {6}}{9}\sqrt { \left ( x-{\it \_C1} \right ) ^{3}}},y \left ( x \right ) =f \left ( {\it \_C1} \right ) +{\frac {2\,\sqrt {6}}{9}\sqrt { \left ( x-{\it \_C1} \right ) ^{3}}} \right \} \]