60.7.57 problem 1665 (book 6.74)

Internal problem ID [11607]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1665 (book 6.74)
Date solved : Sunday, March 30, 2025 at 08:31:26 PM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]]

\begin{align*} x y^{\prime \prime }+2 y^{\prime }+a \,x^{v} y^{n}&=0 \end{align*}

✗ Maple

ode:=x*diff(diff(y(x),x),x)+2*diff(y(x),x)+a*x^v*y(x)^n = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

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

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