22.18 problem 3(b)

Internal problem ID [6493]
Internal file name [OUTPUT/5741_Sunday_June_05_2022_03_52_10_PM_60465236/index.tex]

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).
ODE order: 3.
ODE degree: 1.

The type(s) of ODE detected by this program : "unknown"

Maple gives the following as the ode type

[[_3rd_order, _with_linear_symmetries]]

Unable to solve or complete the solution.

Unable to parse ODE.

Maple trace

`Methods for third order ODEs: 
--- Trying classification methods --- 
trying a quadrature 
checking if the LODE has constant coefficients 
checking if the LODE is of Euler type 
trying high order exact linear fully integrable 
trying to convert to a linear ODE with constant coefficients 
trying differential order: 3; missing the dependent variable 
trying Louvillian solutions for 3rd order ODEs, imprimitive case 
-> pFq: Equivalence to the 3F2 or one of its 3 confluent cases under a power @ Moebius 
<- pFq successful: received ODE is equivalent to the  0F2  ODE, case  c = 0 `
 

✓ Solution by Maple

Time used: 0.11 (sec). Leaf size: 12916

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

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

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 11815

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

Too large to display