54.7.26 problem 1616 (6.26)

Internal problem ID [12875]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1616 (6.26)
Date solved : Wednesday, October 01, 2025 at 02:40:28 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+a y^{\prime }+b y^{n}+\frac {\left (a^{2}-1\right ) y}{4}&=0 \end{align*}

✗ Maple

ode:=diff(diff(y(x),x),x)+a*diff(y(x),x)+b*y(x)^n+1/4*(a^2-1)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=((-1 + a^2)*y[x])/4 + b*y[x]^n + a*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") 
n = symbols("n") 
y = Function("y") 
ode = Eq(a*Derivative(y(x), x) + b*y(x)**n + (a**2 - 1)*y(x)/4 + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (-a**2*y(x)/4 - b*y(x)**n + y(x)/4 - Derivative(y(x), (x, 2)))/a cannot be solved by the factorable group method