57.11.4 problem 1(d)

Internal problem ID [14438]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 2, Second order linear equations. Section 2.4.1 Cauchy-Euler equations. Exercises page 120
Problem number : 1(d)
Date solved : Thursday, October 02, 2025 at 09:37:12 AM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} t x^{\prime \prime }+4 x^{\prime }+\frac {2 x}{t}&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 13

ode:=t*diff(diff(x(t),t),t)+4*diff(x(t),t)+2*x(t)/t = 0; 
dsolve(ode,x(t), singsol=all);
 

\[ x = \frac {c_1 t +c_2}{t^{2}} \]

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 16

ode=t*D[x[t],{t,2}]+4*D[x[t],t]+2/t*x[t]==0; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to \frac {c_2 t+c_1}{t^2} \end{align*}

✓ Sympy. Time used: 0.101 (sec). Leaf size: 8

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(t*Derivative(x(t), (t, 2)) + 4*Derivative(x(t), t) + 2*x(t)/t,0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = \frac {C_{1} + \frac {C_{2}}{t}}{t} \]