13.9.14 problem 19

Internal problem ID [2400]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 2.2.2, Equal roots, reduction of order. Page 147
Problem number : 19
Date solved : Monday, January 27, 2025 at 05:51:39 AM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 14

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

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

✓ Solution by Mathematica

Time used: 0.020 (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]
 

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