\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -a \left ( y \left ( x \right ) \right ) ^{3}-b{x}^{3/2}=0} \]
Mathematica: cpu = 8.692104 (sec), leaf count = 26 \[ \text {DSolve}\left [-a y(x)^3-b x^{3/2}+y'(x)=0,y(x),x\right ] \]
Maple: cpu = 0.655 (sec), leaf count = 0 \[ \text {could not solve} \]
Sage: cpu = 0 (sec), leaf count = 0 \[ \text {Maxima was unable to solve this ODE} \]