82.1.16 problem 23-19

Internal problem ID [21758]
Book : The Differential Equations Problem Solver. VOL. II. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 23. Power series. Page 695
Problem number : 23-19
Date solved : Thursday, October 02, 2025 at 08:01:52 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} x^{\prime \prime }-s x&=0 \end{align*}

Using series method with expansion around

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 47

Order:=6; 
ode:=diff(diff(x(t),t),t)-s*x(t) = 0; 
dsolve(ode,x(t),type='series',t=0);
 

\[ x = \left (1+\frac {1}{2} s \,t^{2}+\frac {1}{24} s^{2} t^{4}\right ) x \left (0\right )+\left (t +\frac {1}{6} s \,t^{3}+\frac {1}{120} s^{2} t^{5}\right ) x^{\prime }\left (0\right )+O\left (t^{6}\right ) \]

✓ Mathematica. Time used: 0.001 (sec). Leaf size: 50

ode=D[x[t],{t,2}]-s*x[t]==0; 
ic={}; 
AsymptoticDSolveValue[{ode,ic},x[t],{t,0,5}]
 

\[ x(t)\to c_2 \left (\frac {s^2 t^5}{120}+\frac {s t^3}{6}+t\right )+c_1 \left (\frac {s^2 t^4}{24}+\frac {s t^2}{2}+1\right ) \]

✗ Sympy

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

ValueError : ODE -s*x(t) + Derivative(x(t), (t, 2)) does not match hint 2nd_power_series_regular