63.11.2 problem 1(b)

Internal problem ID [13076]
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(b)
Date solved : Wednesday, March 05, 2025 at 09:16:40 PM
CAS classification : [[_Emden, _Fowler]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 27

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

\[ x \left (t \right ) = \sqrt {t}\, \left (t^{\frac {\sqrt {17}}{2}} c_{1} +t^{-\frac {\sqrt {17}}{2}} c_{2} \right ) \]

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 34

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

\[ x(t)\to t^{\frac {1}{2}-\frac {\sqrt {17}}{2}} \left (c_2 t^{\sqrt {17}}+c_1\right ) \]

✓ Sympy. Time used: 0.071 (sec). Leaf size: 29

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

\[ x{\left (t \right )} = \frac {C_{1}}{t^{- \frac {1}{2} + \frac {\sqrt {17}}{2}}} + C_{2} t^{\frac {1}{2} + \frac {\sqrt {17}}{2}} \]