90.23.10 problem 14

Internal problem ID [25363]
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 365
Problem number : 14
Date solved : Friday, October 03, 2025 at 12:00:38 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

Using Laplace method

✓ Maple. Time used: 0.055 (sec). Leaf size: 29

ode:=t*diff(diff(y(t),t),t)+2*diff(y(t),t)+9*t*y(t) = 0; 
dsolve(ode,y(t),method='laplace');
 

\[ y = \frac {y \left (0\right ) \sin \left (3 t \right )}{3 t}+\frac {\left (-\pi y \left (0\right )+6 c_1 \right ) \delta \left (t \right )}{6} \]

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 37

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

\begin{align*} y(t)&\to \frac {6 c_1 e^{-3 i t}-i c_2 e^{3 i t}}{6 t} \end{align*}

✓ Sympy. Time used: 0.127 (sec). Leaf size: 24

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

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