54.7.27 problem 1617 (6.27)

Internal problem ID [12876]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1617 (6.27)
Date solved : Wednesday, October 01, 2025 at 02:43:38 AM
CAS classification : [NONE]

\begin{align*} y^{\prime \prime }+a y^{\prime }+b \,x^{v} y^{n}&=0 \end{align*}

✗ Maple

ode:=diff(diff(y(x),x),x)+a*diff(y(x),x)+b*x^v*y(x)^n = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=b*x^v*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") 
v = symbols("v") 
y = Function("y") 
ode = Eq(a*Derivative(y(x), x) + b*x**v*y(x)**n + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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