90.22.3 problem 3

Internal problem ID [25341]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 5. Second Order Linear Differential Equations. Exercises at page 353
Problem number : 3
Date solved : Friday, October 03, 2025 at 12:00:23 AM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} 9 t^{2} y^{\prime \prime }+3 t y^{\prime }+y&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 14

ode:=9*t^2*diff(diff(y(t),t),t)+3*t*diff(y(t),t)+y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \left (\ln \left (t \right ) c_2 +c_1 \right ) t^{{1}/{3}} \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 24

ode=9*t^2*D[y[t],{t,2}]+3*t*D[y[t],t]+y[t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {1}{3} \sqrt [3]{t} (c_2 \log (t)+3 c_1) \end{align*}

✓ Sympy. Time used: 0.105 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(9*t**2*Derivative(y(t), (t, 2)) + 3*t*Derivative(y(t), t) + y(t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \sqrt [3]{t} \left (C_{1} + C_{2} \log {\left (t \right )}\right ) \]