23.4.4 problem 4

Internal problem ID [6306]
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 : 4
Date solved : Tuesday, September 30, 2025 at 02:45:39 PM
CAS classification : [[_Painleve, `1st`]]

\begin{align*} y^{\prime \prime }&=x +6 y^{2} \end{align*}

✗ Maple

ode:=diff(diff(y(x),x),x) = x+6*y(x)^2; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[y[x],{x,2}] == x + 6*y[x]^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x - 6*y(x)**2 + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : solve: Cannot solve -x - 6*y(x)**2 + Derivative(y(x), (x, 2))