63.1.8 problem 8

Internal problem ID [12953]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 1, First order differential equations. Section 1.1 First order equations. Exercises page 10
Problem number : 8
Date solved : Wednesday, March 05, 2025 at 08:54:45 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} t^{2} x^{\prime \prime }-6 x&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 15

ode:=t^2*diff(diff(x(t),t),t)-6*x(t) = 0; 
dsolve(ode,x(t), singsol=all);
 

\[ x \left (t \right ) = \frac {c_{1} t^{5}+c_{2}}{t^{2}} \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 18

ode=t^2*D[x[t],{t,2}]-6*x[t]==0; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\[ x(t)\to \frac {c_2 t^5+c_1}{t^2} \]

✓ Sympy. Time used: 0.053 (sec). Leaf size: 12

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(t**2*Derivative(x(t), (t, 2)) - 6*x(t),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = \frac {C_{1}}{t^{2}} + C_{2} t^{3} \]