63.11.5 problem 1(e)

Internal problem ID [13158]
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(e)
Date solved : Tuesday, January 28, 2025 at 05:11:26 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} t^{2} x^{\prime \prime }-7 t x^{\prime }+16 x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 14

dsolve(t^2*diff(x(t),t$2)-7*t*diff(x(t),t)+16*x(t)=0,x(t), singsol=all)
 

\[ x \left (t \right ) = t^{4} \left (c_{2} \ln \left (t \right )+c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 18

DSolve[t^2*D[x[t],{t,2}]-7*t*D[x[t],t]+16*x[t]==0,x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to t^4 (4 c_2 \log (t)+c_1) \]