23.4.34 problem 34

Internal problem ID [6336]
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 : 34
Date solved : Tuesday, September 30, 2025 at 02:51:41 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} b y+a \left (-1+y^{2}\right ) y^{\prime }+y^{\prime \prime }&=0 \end{align*}

✗ Maple

ode:=b*y(x)+a*(y(x)^2-1)*diff(y(x),x)+diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=b*y[x] + a*(-1 + y[x]^2)*D[y[x],x] + 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") 
b = symbols("b") 
y = Function("y") 
ode = Eq(a*(y(x)**2 - 1)*Derivative(y(x), x) + b*y(x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (-b*y(x) - Derivative(y(x), (x, 2)))/(a*(y