63.11.1 problem 1(a)

Internal problem ID [13154]
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(a)
Date solved : Tuesday, January 28, 2025 at 05:11:19 AM
CAS classification : [[_Emden, _Fowler]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 29

dsolve(diff(x(t),t$2)=-1/t^2*x(t),x(t), singsol=all)
 

\[ x \left (t \right ) = \sqrt {t}\, \left (c_{1} \sin \left (\frac {\sqrt {3}\, \ln \left (t \right )}{2}\right )+c_{2} \cos \left (\frac {\sqrt {3}\, \ln \left (t \right )}{2}\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 42

DSolve[D[x[t],{t,2}]==-1/t^2*x[t],x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \sqrt {t} \left (c_1 \cos \left (\frac {1}{2} \sqrt {3} \log (t)\right )+c_2 \sin \left (\frac {1}{2} \sqrt {3} \log (t)\right )\right ) \]