73.9.4 problem 14.1 (d)

Internal problem ID [15194]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 14. Higher order equations and the reduction of order method. Additional exercises page 277
Problem number : 14.1 (d)
Date solved : Monday, March 31, 2025 at 01:31:01 PM
CAS classification : [NONE]

\begin{align*} y^{\prime \prime }+x^{2} y^{\prime }+4 y&=y^{3} \end{align*}

✗ Maple

ode:=diff(diff(y(x),x),x)+x^2*diff(y(x),x)+4*y(x) = y(x)^3; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[y[x],{x,2}]+x^2*D[y[x],x]+4*y[x]==y[x]^3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), x) - y(x)**3 + 4*y(x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (y(x)**3 - 4*y(x) - Derivative(y(x), (x, 2)))/x**2 cannot be solved by the factorable group method