60.7.6 problem 1596 (6.6)

Internal problem ID [11556]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1596 (6.6)
Date solved : Sunday, March 30, 2025 at 08:25:00 PM
CAS classification : [[_Painleve, `2nd`]]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

NotImplementedError : solve: Cannot solve a - x*y(x) - 2*y(x)**3 + Derivative(y(x), (x, 2))