74.1.5 problem 6

Internal problem ID [15785]
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 : 6
Date solved : Tuesday, January 28, 2025 at 08:07:10 AM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

Time used: 0.026 (sec). Leaf size: 30

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

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