63.11.8 problem 1(h)

Internal problem ID [13161]
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(h)
Date solved : Tuesday, January 28, 2025 at 05:11:30 AM
CAS classification : [[_Emden, _Fowler]]

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

With initial conditions

\begin{align*} x \left (1\right )&=0\\ x^{\prime }\left (1\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 9

dsolve([t^2*diff(x(t),t$2)-t*diff(x(t),t)+2*x(t)=0,x(1) = 0, D(x)(1) = 1],x(t), singsol=all)
 

\[ x \left (t \right ) = t \sin \left (\ln \left (t \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 10

DSolve[{t^2*D[x[t],{t,2}]-t*D[x[t],t]+2*x[t]==0,{x[1]==0,Derivative[1][x][1 ]==1}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to t \sin (\log (t)) \]