36.1.23 problem 3.50

Internal problem ID [8131]
Book : Advanced Mathematical Methods for Scientists and Engineers, Bender and Orszag. Springer October 29, 1999
Section : Chapter 3. APPROXIMATE SOLUTION OF LINEAR DIFFERENTIAL EQUATIONS. page 136
Problem number : 3.50
Date solved : Tuesday, September 30, 2025 at 05:15:57 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }-\frac {y}{x}&=\cos \left (x \right ) \end{align*}

Using series method with expansion around

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

✗ Maple

Order:=6; 
ode:=diff(y(x),x)-y(x)/x = cos(x); 
dsolve(ode,y(x),type='series',x=0);
 

\[ \text {No solution found} \]

✓ Mathematica. Time used: 0.037 (sec). Leaf size: 34

ode=D[y[x],x]-y[x]/x==Cos[x]; 
ic={}; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,0,5}]
 

\[ y(x)\to x \left (-\frac {x^6}{4320}+\frac {x^4}{96}-\frac {x^2}{4}+\log (x)\right )+c_1 x \]

✗ Sympy

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

ValueError : ODE -cos(x) + Derivative(y(x), x) - y(x)/x does not match hint 1st_power_series