63.11.3 problem 1(c)

Internal problem ID [13156]
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(c)
Date solved : Tuesday, January 28, 2025 at 05:11:22 AM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 14

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

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

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 17

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

\[ x(t)\to \frac {c_2 \log (t)+c_1}{t} \]