\[ \boxed { \left ( {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) \right ) \sqrt {x}- \left ( y \left ( x \right ) \right ) ^{3/2}=0} \]
Mathematica: cpu = 22.744388 (sec), leaf count = 25 \[ \text {DSolve}\left [\sqrt {x} y''(x)-y(x)^{3/2}=0,y(x),x\right ] \]
Maple: cpu = 3.479 (sec), leaf count = 97 \[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {\frac {{\it \_a }}{ \left ( {{\rm e}^{\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}}} \right ) ^{3}}},[ \left \{ {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) = \left ( -{{\it \_a}}^{{\frac {3}{2}}}+12\,{\it \_a} \right ) \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{3}-7\, \left ( {\it \_b} \left ( { \it \_a} \right ) \right ) ^{2} \right \} , \left \{ {\it \_a}={x}^{3}y \left ( x \right ) ,{\it \_b} \left ( {\it \_a} \right ) ={\frac {1}{{x}^ {3} \left ( x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +3\,y \left ( x \right ) \right ) }} \right \} , \left \{ x={{\rm e}^{\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}}},y \left ( x \right ) ={\frac {{\it \_a}}{ \left ( {{\rm e}^{\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}}} \right ) ^{3} }} \right \} ] \right ) \right \} \]