63.11.7 problem 1(g)

Internal problem ID [13081]
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 : Wednesday, March 05, 2025 at 09:16:48 PM
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*}

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

ode:=t^2*diff(diff(x(t),t),t)+t*diff(x(t),t) = 0; 
ic:=x(1) = 0, D(x)(1) = 2; 
dsolve([ode,ic],x(t), singsol=all);
 

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

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

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

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

✓ Sympy. Time used: 0.139 (sec). Leaf size: 7

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(t**2*Derivative(x(t), (t, 2)) + t*Derivative(x(t), t),0) 
ics = {x(1): 0, Subs(Derivative(x(t), t), t, 1): 2} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = 2 \log {\left (t \right )} \]