58.22.7 problem 3(c)

Internal problem ID [14953]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 11, The nth order homogeneous linear differential equation. Section 11.8, Exercises page 583
Problem number : 3(c)
Date solved : Thursday, October 02, 2025 at 09:56:57 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \frac {\left (t +1\right ) x^{\prime \prime }}{t}-\frac {x^{\prime }}{t^{2}}+\frac {x}{t^{3}}&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 19

ode:=(t+1)/t*diff(diff(x(t),t),t)-1/t^2*diff(x(t),t)+1/t^3*x(t) = 0; 
dsolve(ode,x(t), singsol=all);
 

\[ x = t \left (c_2 \ln \left (t \right )-c_2 \ln \left (t +1\right )+c_1 \right ) \]

✓ Mathematica. Time used: 0.023 (sec). Leaf size: 22

ode=(t+1)/t*D[x[t],{t,2}]-1/t^2*D[x[t],t]+1/t^3*x[t]==0; 
ic={}; 
DSolve[{ode,ic},{x[t]},t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to t (c_2 (\log (t)-\log (t+1))+c_1) \end{align*}

✗ Sympy

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq((t + 1)*Derivative(x(t), (t, 2))/t - Derivative(x(t), t)/t**2 + x(t)/t**3,0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

False