10.9.30 problem 45

Internal problem ID [1332]
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 : 45
Date solved : Monday, January 27, 2025 at 04:51:12 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} t^{2} y^{\prime \prime }+5 t y^{\prime }+13 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 23

dsolve(t^2*diff(y(t),t$2)+5*t*diff(y(t),t)+13*y(t)=0,y(t), singsol=all)
 

\[ y = \frac {c_1 \sin \left (3 \ln \left (t \right )\right )+c_2 \cos \left (3 \ln \left (t \right )\right )}{t^{2}} \]

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 26

DSolve[t^2*D[y[t],{t,2}]+5*t*D[y[t],t]+13*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {c_2 \cos (3 \log (t))+c_1 \sin (3 \log (t))}{t^2} \]