90.23.12 problem 16

Internal problem ID [25365]
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 : 16
Date solved : Friday, October 03, 2025 at 12:00:39 AM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

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

Using Laplace method

✓ Maple. Time used: 0.042 (sec). Leaf size: 23

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

\[ y = c_1 \delta \left (t \right )+\frac {y \left (0\right ) \left (1-{\mathrm e}^{-t}\right )}{t} \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 20

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

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

✗ Sympy

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

False