23.4.7 problem 7

Internal problem ID [6309]
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 : 7
Date solved : Tuesday, September 30, 2025 at 02:45:42 PM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

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

✓ Maple. Time used: 0.008 (sec). Leaf size: 63

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

\begin{align*} \int _{}^{y}\frac {1}{\sqrt {\textit {\_a}^{4}+\textit {\_a}^{2} b +2 \textit {\_a} a +c_1}}d \textit {\_a} -x -c_2 &= 0 \\ -\int _{}^{y}\frac {1}{\sqrt {\textit {\_a}^{4}+\textit {\_a}^{2} b +2 \textit {\_a} a +c_1}}d \textit {\_a} -x -c_2 &= 0 \\ \end{align*}

✓ Mathematica. Time used: 0.535 (sec). Leaf size: 664

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

\begin{align*} \text {Solution too large to show}\end{align*}

✗ Sympy

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

Timed Out