10.9.19 problem 25

Internal problem ID [1321]
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 : 25
Date solved : Monday, January 27, 2025 at 04:51:00 AM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} t^{2} y^{\prime \prime }+3 t y^{\prime }+y&=0 \end{align*}

Using reduction of order method given that one solution is

\begin{align*} y&=\frac {1}{t} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 14

dsolve([t^2*diff(y(t),t$2)+3*t*diff(y(t),t)+y(t)=0,1/t],singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 17

DSolve[t^2*D[y[t],{t,2}]+3*t*D[y[t],t]+y[t]==0,y[t],t,IncludeSingularSolutions -> True]
 

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