63.11.2 problem 1(b)

Internal problem ID [13155]
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 : Tuesday, January 28, 2025 at 05:11:21 AM
CAS classification : [[_Emden, _Fowler]]

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

✓ Solution by Maple

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

dsolve(diff(x(t),t$2)=4/t^2*x(t),x(t), singsol=all)
 

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

✓ Solution by Mathematica

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

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

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