50.5.10 problem 10

Internal problem ID [10257]
Book : Own collection of miscellaneous problems
Section : section 5.0
Problem number : 10
Date solved : Tuesday, September 30, 2025 at 07:16:00 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=\frac {1}{x} \end{align*}

Using series method with expansion around

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

✗ Maple

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

\[ \text {No solution found} \]

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 8

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

\[ y(x)\to \log (x)+c_1 \]

✗ Sympy

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

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