46.1.15 problem 13

Internal problem ID [9518]
Book : DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL, WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th edition.
Section : CHAPTER 6 SERIES SOLUTIONS OF LINEAR EQUATIONS. Section 6.2 SOLUTIONS ABOUT ORDINARY POINTS. EXERCISES 6.2. Page 246
Problem number : 13
Date solved : Tuesday, September 30, 2025 at 06:19:59 PM
CAS classification : [[_2nd_order, _missing_y]]

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

Using series method with expansion around

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

✓ Maple. Time used: 0.010 (sec). Leaf size: 46

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

\[ y = y \left (0\right )+\left (x +\frac {1}{2} x^{2}+\frac {1}{3} x^{3}+\frac {1}{4} x^{4}+\frac {1}{5} x^{5}+\frac {1}{6} x^{6}+\frac {1}{7} x^{7}\right ) y^{\prime }\left (0\right )+O\left (x^{8}\right ) \]

✓ Mathematica. Time used: 0.001 (sec). Leaf size: 53

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

\[ y(x)\to c_2 \left (\frac {x^7}{7}+\frac {x^6}{6}+\frac {x^5}{5}+\frac {x^4}{4}+\frac {x^3}{3}+\frac {x^2}{2}+x\right )+c_1 \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((x - 1)*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=8)
 

IndexError : list index out of range