88.25.3 problem 2 (c)

Internal problem ID [24208]
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 (c)
Date solved : Friday, October 03, 2025 at 08:03:53 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

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

Using series method with expansion around

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

✓ Maple. Time used: 0.012 (sec). Leaf size: 235

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

\[ y = c_2 \,x^{\frac {\sqrt {5}}{2}+\frac {3}{2}} \left (1+\frac {1}{-5-3 \sqrt {5}} x +\frac {1}{230+102 \sqrt {5}} x^{2}-\frac {1}{9036 \sqrt {5}+20220} x^{3}+\frac {1}{3336960+1492128 \sqrt {5}} x^{4}-\frac {1}{60} \frac {1}{\left (5+3 \sqrt {5}\right ) \left (9 \sqrt {5}+19\right ) \left (3 \sqrt {5}+8\right ) \left (15 \sqrt {5}+49\right ) \left (9 \sqrt {5}+35\right )} x^{5}+\operatorname {O}\left (x^{6}\right )\right )+c_1 \,x^{-\frac {\sqrt {5}}{2}+\frac {3}{2}} \left (1+\frac {1}{3 \sqrt {5}-5} x +\frac {1}{230-102 \sqrt {5}} x^{2}+\frac {1}{9036 \sqrt {5}-20220} x^{3}+\frac {1}{3336960-1492128 \sqrt {5}} x^{4}+\frac {1}{60} \frac {1}{\left (3 \sqrt {5}-5\right ) \left (9 \sqrt {5}-19\right ) \left (3 \sqrt {5}-8\right ) \left (15 \sqrt {5}-49\right ) \left (9 \sqrt {5}-35\right )} x^{5}+\operatorname {O}\left (x^{6}\right )\right )+c_3 \left (1+x +\frac {1}{2} x^{2}-\frac {1}{6} x^{3}+\frac {1}{120} x^{4}-\frac {1}{6600} x^{5}+\operatorname {O}\left (x^{6}\right )\right ) \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 1834

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

Too large to display

✗ 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