64.14.9 problem 9

Internal problem ID [13568]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 6, Series solutions of linear differential equations. Section 6.1. Exercises page 232
Problem number : 9
Date solved : Tuesday, January 28, 2025 at 05:53:06 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 29

Order:=6; 
dsolve((x^3-1)*diff(y(x),x$2)+x^2*diff(y(x),x)+x*y(x)=0,y(x),type='series',x=0);
 

\[ y = \left (1+\frac {x^{3}}{6}\right ) y \left (0\right )+\left (x +\frac {1}{6} x^{4}\right ) y^{\prime }\left (0\right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 28

AsymptoticDSolveValue[(x^3-1)*D[y[x],{x,2}]+x^2*D[y[x],x]+x*y[x]==0,y[x],{x,0,"6"-1}]
 

\[ y(x)\to c_2 \left (\frac {x^4}{6}+x\right )+c_1 \left (\frac {x^3}{6}+1\right ) \]