64.22.1 problem 1 (a)

Internal problem ID [13666]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 11, The nth order homogeneous linear differential equation. Section 11.8, Exercises page 583
Problem number : 1 (a)
Date solved : Tuesday, January 28, 2025 at 05:54:35 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} t^{2} x^{\prime \prime }+3 t x^{\prime }+3 x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 27

dsolve(t^2*diff(x(t),t$2)+3*t*diff(x(t),t)+3*x(t)=0,x(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 34

DSolve[t^2*D[x[t],{t,2}]+3*t*D[x[t],t]+3*x[t]==0,{x[t]},t,IncludeSingularSolutions -> True]
 

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