64.14.8 problem 8

Internal problem ID [13567]
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 : 8
Date solved : Tuesday, January 28, 2025 at 05:53:05 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 52

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

\[ y = \left (1+\frac {1}{3} x^{3}+\frac {1}{3} x^{4}+\frac {11}{60} x^{5}\right ) y \left (0\right )+\left (x +x^{2}+\frac {1}{2} x^{3}+\frac {1}{6} x^{4}+\frac {1}{24} x^{5}\right ) y^{\prime }\left (0\right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 59

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

\[ y(x)\to c_1 \left (\frac {11 x^5}{60}+\frac {x^4}{3}+\frac {x^3}{3}+1\right )+c_2 \left (\frac {x^5}{24}+\frac {x^4}{6}+\frac {x^3}{2}+x^2+x\right ) \]