90.25.7 problem 7

Internal problem ID [25388]
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 379
Problem number : 7
Date solved : Friday, October 03, 2025 at 12:00:49 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }+y&=\frac {{\mathrm e}^{t}}{t} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 18

ode:=diff(diff(y(t),t),t)-2*diff(y(t),t)+y(t) = exp(t)/t; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \left (\ln \left (t \right ) t +t \left (c_1 -1\right )+c_2 \right ) {\mathrm e}^{t} \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 22

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

\begin{align*} y(t)&\to e^t (t \log (t)+(-1+c_2) t+c_1) \end{align*}

✓ Sympy. Time used: 0.146 (sec). Leaf size: 14

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

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