Internal problem ID [14065]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {t^{2} y^{\prime \prime }+3 y^{\prime } t +5 y=0} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (t \right ) = \frac {c_{1} \sin \left (2 \ln \left (t \right )\right )+c_{2} \cos \left (2 \ln \left (t \right )\right )}{t} \]
✓ Solution by Mathematica
Time used: 0.028 (sec). Leaf size: 26
DSolve[t^2*y''[t]+3*t*y'[t]+5*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {c_2 \cos (2 \log (t))+c_1 \sin (2 \log (t))}{t} \]