63.11.7 problem 1(g)

Internal problem ID [13160]
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(g)
Date solved : Tuesday, January 28, 2025 at 05:11:29 AM
CAS classification : [[_2nd_order, _missing_y]]

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

With initial conditions

\begin{align*} x \left (1\right )&=0\\ x^{\prime }\left (1\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 8

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

\[ x \left (t \right ) = 2 \ln \left (t \right ) \]

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 9

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

\[ x(t)\to 2 \log (t) \]