13.9.15 problem 20

Internal problem ID [2401]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 2.2.2, Equal roots, reduction of order. Page 147
Problem number : 20
Date solved : Monday, January 27, 2025 at 05:51:40 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} t^{2} y^{\prime \prime }-t y^{\prime }+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: 0.024 (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]
 

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