90.23.7 problem 11

Internal problem ID [25360]
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 : 11
Date solved : Friday, October 03, 2025 at 12:00:37 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: 0.041 (sec). Leaf size: 19

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: 0.01 (sec). Leaf size: 18

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

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