74.1.21 problem 28

Internal problem ID [15801]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 1. Introduction to Differential Equations. Exercises 1.1, page 10
Problem number : 28
Date solved : Tuesday, January 28, 2025 at 08:07:38 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} t^{2} y^{\prime \prime }+3 y^{\prime } t +5 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 23

dsolve(t^2*diff(y(t),t$2)+3*t*diff(y(t),t)+5*y(t)=0,y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.028 (sec). Leaf size: 26

DSolve[t^2*D[y[t],{t,2}]+3*t*D[y[t],t]+5*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
 

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