63.1.8 problem 8

Internal problem ID [13032]
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 : Tuesday, January 28, 2025 at 04:49:47 AM
CAS classification : [[_Emden, _Fowler]]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

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

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

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