54.7.82 problem 1691 (book 6.100)

Internal problem ID [12931]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1691 (book 6.100)
Date solved : Wednesday, October 01, 2025 at 02:46:19 AM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime } \sqrt {x}-y^{{3}/{2}}&=0 \end{align*}

✗ Maple

ode:=diff(diff(y(x),x),x)*x^(1/2)-y(x)^(3/2) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=-y[x]^(3/2) + Sqrt[x]*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(sqrt(x)*Derivative(y(x), (x, 2)) - y(x)**(3/2),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : solve: Cannot solve sqrt(x)*Derivative(y(x), (x, 2)) - y(x)**(3/2)