90.20.11 problem 11

Internal problem ID [25306]
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 337
Problem number : 11
Date solved : Thursday, October 02, 2025 at 11:59:49 PM
CAS classification : [_Bessel]

\begin{align*} t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-5\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 19

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

\[ y = c_1 \operatorname {BesselJ}\left (\sqrt {5}, t\right )+c_2 \operatorname {BesselY}\left (\sqrt {5}, t\right ) \]

✓ Mathematica. Time used: 0.062 (sec). Leaf size: 26

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

\begin{align*} y(t)&\to c_1 \operatorname {BesselJ}\left (\sqrt {5},t\right )+c_2 \operatorname {BesselY}\left (\sqrt {5},t\right ) \end{align*}

✓ Sympy. Time used: 0.123 (sec). Leaf size: 19

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

\[ y{\left (t \right )} = C_{1} J_{\sqrt {5}}\left (t\right ) + C_{2} Y_{\sqrt {5}}\left (t\right ) \]