23.4.117 problem 117

Internal problem ID [6419]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 4. THE NONLINEAR EQUATION OF SECOND ORDER, page 380
Problem number : 117
Date solved : Tuesday, September 30, 2025 at 02:56:28 PM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

ode=Sqrt[x]*D[y[x],{x,2}] == y[x]^(3/2); 
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)