88.25.5 problem 2 (e)

Internal problem ID [24210]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 7. Series Methods. Exercises at page 212
Problem number : 2 (e)
Date solved : Thursday, October 02, 2025 at 10:00:50 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} x^{4} y^{\prime \prime \prime }-\frac {x^{2} y^{\prime }}{1+x}+y&=0 \end{align*}

Using series method with expansion around

\begin{align*} 0 \end{align*}

✗ Maple

Order:=6; 
ode:=x^4*diff(diff(diff(y(x),x),x),x)-x^2/(1+x)*diff(y(x),x)+y(x) = 0; 
dsolve(ode,y(x),type='series',x=0);
 

\[ \text {No solution found} \]

✓ Mathematica. Time used: 0.226 (sec). Leaf size: 540

ode=x^4*D[y[x],{x,3}]-x^2/(1+x)*D[y[x],{x,1}]+y[x]==0; 
ic={}; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,0,5}]
 

\begin{align*} \text {Solution too large to show}\end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**2*y(x) + x*Derivative(y(x), (x, 2)) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics,hint="2nd_power_series_regular",x0=0,n=6)
 

Series solution not supported for ode of order > 2