23.4.11 problem 11

Internal problem ID [6313]
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 : 11
Date solved : Tuesday, September 30, 2025 at 02:45:45 PM
CAS classification : [NONE]

\begin{align*} y^{\prime \prime }&=\operatorname {a0} +\operatorname {a2} y+\operatorname {a1} x y+\operatorname {a3} y^{3} \end{align*}

✗ Maple

ode:=diff(diff(y(x),x),x) = a0+a2*y(x)+a1*x*y(x)+a3*y(x)^3; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[y[x],{x,2}] == a0 + a2*y[x] + a1*x*y[x] + a3*y[x]^3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
a0 = symbols("a0") 
a1 = symbols("a1") 
a2 = symbols("a2") 
a3 = symbols("a3") 
y = Function("y") 
ode = Eq(-a0 - a1*x*y(x) - a2*y(x) - a3*y(x)**3 + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : solve: Cannot solve -a0 - a1*x*y(x) - a2*y(x) - a3*y(x)**3 + Derivative(y(x),