64.22.8 problem 4(a)

Internal problem ID [13673]
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 : 4(a)
Date solved : Tuesday, January 28, 2025 at 05:54:47 AM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 15

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

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

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 18

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

\[ x(t)\to c_1 \cos (\log (t))+c_2 \sin (\log (t)) \]