50.22.18 problem 3(b)

Internal problem ID [8161]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 4. Power Series Solutions and Special Functions. Problems for review and discovert. (A) Drill Exercises . Page 194
Problem number : 3(b)
Date solved : Sunday, March 30, 2025 at 12:47:03 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-3 x y^{\prime }+\left (x -1\right ) y&=0 \end{align*}

Using series method with expansion around

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

✓ Maple. Time used: 0.045 (sec). Leaf size: 2653

Order:=8; 
ode:=x^3*diff(diff(diff(y(x),x),x),x)+x^2*diff(diff(y(x),x),x)-3*x*diff(y(x),x)+(x-1)*y(x) = 0; 
dsolve(ode,y(x),type='series',x=0);
 

\[ \text {Expression too large to display} \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 11815

ode=x^3*D[y[x],{x,3}]+x^2*D[y[x],{x,2}]-3*x*D[y[x],x]+(x-1)*y[x]==0; 
ic={}; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,0,7}]
 

Too large to display

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) + x*(1 - x)*Derivative(y(x), x) + y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics,hint="2nd_power_series_regular",x0=0,n=8)
 

Series solution not supported for ode of order > 2