76.12.19 problem 31

Internal problem ID [17575]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.2 (Theory of second order linear homogeneous equations). Problems at page 226
Problem number : 31
Date solved : Tuesday, January 28, 2025 at 10:44:25 AM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} t^{2} y^{\prime \prime }+3 y^{\prime } t +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: 0.003 (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: 0.015 (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]
 

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