64.22.5 problem 3(a)

Internal problem ID [13670]
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 : 3(a)
Date solved : Tuesday, January 28, 2025 at 05:54:42 AM
CAS classification : [[_Emden, _Fowler]]

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

✓ Solution by Maple

Time used: 0.052 (sec). Leaf size: 53

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

\[ x \left (t \right ) = \frac {\sqrt {t}\, \operatorname {BesselJ}\left (1, \frac {2}{\sqrt {t}}\right ) c_{1} +\sqrt {t}\, \operatorname {BesselY}\left (1, \frac {2}{\sqrt {t}}\right ) c_{2} -\operatorname {BesselJ}\left (0, \frac {2}{\sqrt {t}}\right ) c_{1} -\operatorname {BesselY}\left (0, \frac {2}{\sqrt {t}}\right ) c_{2}}{t} \]

✓ Solution by Mathematica

Time used: 0.055 (sec). Leaf size: 40

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

\[ x(t)\to \frac {2 c_1 \operatorname {BesselJ}\left (2,2 \sqrt {\frac {1}{t}}\right )-2 c_2 \operatorname {BesselY}\left (2,2 \sqrt {\frac {1}{t}}\right )}{t} \]