60.7.3 problem 1593 (6.3)

Internal problem ID [11553]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1593 (6.3)
Date solved : Sunday, March 30, 2025 at 08:24:53 PM
CAS classification : [[_Painleve, `1st`]]

\begin{align*} y^{\prime \prime }-6 y^{2}-x&=0 \end{align*}

✗ Maple

ode:=diff(diff(y(x),x),x)-6*y(x)^2-x = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=-x - 6*y[x]^2 + 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(-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))