57.11.5 problem 1(e)

Internal problem ID [14439]
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(e)
Date solved : Thursday, October 02, 2025 at 09:37:13 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} t^{2} x^{\prime \prime }-7 x^{\prime } t +16 x&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 14

ode:=t^2*diff(diff(x(t),t),t)-7*t*diff(x(t),t)+16*x(t) = 0; 
dsolve(ode,x(t), singsol=all);
 

\[ x = t^{4} \left (c_1 +c_2 \ln \left (t \right )\right ) \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 18

ode=t^2*D[x[t],{t,2}]-7*t*D[x[t],t]+16*x[t]==0; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to t^4 (4 c_2 \log (t)+c_1) \end{align*}

✓ Sympy. Time used: 0.094 (sec). Leaf size: 12

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(t**2*Derivative(x(t), (t, 2)) - 7*t*Derivative(x(t), t) + 16*x(t),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = t^{4} \left (C_{1} + C_{2} \log {\left (t \right )}\right ) \]