10.9.26 problem 41

Internal problem ID [1328]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Chapter 3, Second order linear equations, 3.4 Repeated roots, reduction of order , page 172
Problem number : 41
Date solved : Monday, January 27, 2025 at 04:51:05 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} t^{2} y^{\prime \prime }+2 t y^{\prime }+\frac {y}{4}&=0 \end{align*}

✓ Solution by Maple

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

dsolve(t^2*diff(y(t),t$2)+2*t*diff(y(t),t)+25/100*y(t)=0,y(t), singsol=all)
 

\[ y = \frac {c_2 \ln \left (t \right )+c_1}{\sqrt {t}} \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 24

DSolve[t^2*D[y[t],{t,2}]+2*t*D[y[t],t]+25/100*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {c_2 \log (t)+2 c_1}{2 \sqrt {t}} \]