ODE
\[ \sqrt {x} y''(x)=y(x)^{3/2} \] ODE Classification
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✗
cpu = 22.3749 (sec), leaf count = 0 , could not solve
DSolve[Sqrt[x]*Derivative[2][y][x] == y[x]^(3/2), y[x], x]
Maple ✓
cpu = 0.661 (sec), leaf count = 99
\[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {\frac {{\it \_a}}{ \left ( {{\rm e}^{\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}}} \right ) ^{3}}},[ \left \{ {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) =- \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{3}{{\it \_a}}^{{\frac {3}{2}}}+12\, \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{3}{\it \_a}-7\, \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{2} \right \} , \left \{ {\it \_a}={x}^{3}y \left ( x \right ) ,{\it \_b} \left ( {\it \_a} \right ) ={\frac {1}{{x}^{3} \left ( x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +3\,y \left ( x \right ) \right ) }} \right \} , \left \{ x={{\rm e}^{\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}}},y \left ( x \right ) ={\frac {{\it \_a}}{ \left ( {{\rm e}^{\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}}} \right ) ^{3}}} \right \} ] \right ) \right \} \] Mathematica raw input
DSolve[Sqrt[x]*y''[x] == y[x]^(3/2),y[x],x]
Mathematica raw output
DSolve[Sqrt[x]*Derivative[2][y][x] == y[x]^(3/2), y[x], x]
Maple raw input
dsolve(diff(diff(y(x),x),x)*x^(1/2) = y(x)^(3/2), y(x),'implicit')
Maple raw output
y(x) = ODESolStruc(_a/exp(Int(_b(_a),_a)+_C1)^3,[{diff(_b(_a),_a) = -_b(_a)^3*_a^(3/2)+12*_b(_a)^3*_a-7*_b(_a)^2}, {_a = x^3*y(x), _b(_a) = 1/x^3/(x*diff(y(x),x)+3*y(x))}, {x = exp(Int(_b(_a),_a)+_C1), y(x) = _a/exp(Int(_b(_a),_a)+_C1)^3}])