56.5.11 problem 11

Internal problem ID [8972]
Book : Own collection of miscellaneous problems
Section : section 5.0
Problem number : 11
Date solved : Sunday, March 30, 2025 at 01:57:37 PM
CAS classification : [[_2nd_order, _quadrature]]

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

Using series method with expansion around

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

✗ Maple

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

\[ \text {No solution found} \]

✓ Mathematica. Time used: 0.03 (sec). Leaf size: 17

ode=D[y[x],{x,2}]==1/x; 
ic={}; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,0,5}]
 

\[ y(x)\to -x+x \log (x)+c_2 x+c_1 \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), (x, 2)) - 1/x,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics,hint="2nd_power_series_regular",x0=0,n=6)
 

ValueError : ODE Derivative(y(x), (x, 2)) - 1/x does not match hint 2nd_power_series_regular