68.1.21 problem 28

Internal problem ID [17088]
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 : Thursday, October 02, 2025 at 01:42:51 PM
CAS classification : [[_Emden, _Fowler]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 23

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

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

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 26

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

\begin{align*} y(t)&\to \frac {c_2 \cos (2 \log (t))+c_1 \sin (2 \log (t))}{t} \end{align*}

✓ Sympy. Time used: 0.115 (sec). Leaf size: 20

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(t**2*Derivative(y(t), (t, 2)) + 3*t*Derivative(y(t), t) + 5*y(t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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