74.10.36 problem 37 (b)

Internal problem ID [16241]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.2, page 147
Problem number : 37 (b)
Date solved : Tuesday, January 28, 2025 at 08:58:25 AM
CAS classification : [[_Emden, _Fowler]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 12

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

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

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 15

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

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