73.24.14 problem 34.6 (d)

Internal problem ID [15623]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 34. Power series solutions II: Generalization and theory. Additional Exercises. page 678
Problem number : 34.6 (d)
Date solved : Monday, March 31, 2025 at 01:43:15 PM
CAS classification : [_separable]

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

Using series method with expansion around

\begin{align*} 1 \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 42

Order:=6; 
ode:=diff(y(x),x)+ln(x)*y(x) = 0; 
dsolve(ode,y(x),type='series',x=1);
 

\[ y = \left (1-\frac {\left (x -1\right )^{2}}{2}+\frac {\left (x -1\right )^{3}}{6}+\frac {\left (x -1\right )^{4}}{24}-\frac {\left (x -1\right )^{5}}{30}\right ) y \left (1\right )+O\left (x^{6}\right ) \]

✓ Mathematica. Time used: 0.001 (sec). Leaf size: 44

ode=D[y[x],x]+Log[x]*y[x]==0; 
ic={}; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,1,5}]
 

\[ y(x)\to c_1 \left (-\frac {1}{30} (x-1)^5+\frac {1}{24} (x-1)^4+\frac {1}{6} (x-1)^3-\frac {1}{2} (x-1)^2+1\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x)*log(x) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics,hint="1st_power_series",x0=1,n=6)
 

ValueError : ODE y(x)*log(x) + Derivative(y(x), x) does not match hint 1st_power_series