68.12.20 problem 20

Internal problem ID [17614]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.4, page 163
Problem number : 20
Date solved : Thursday, October 02, 2025 at 02:26:17 PM
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: 0.005 (sec). Leaf size: 18

ode:=diff(diff(y(t),t),t)-2*diff(y(t),t)+y(t) = 1/t*exp(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: 0.014 (sec). Leaf size: 22

ode=D[y[t],{t,2}]-2*D[y[t],t]+y[t]==1/t*Exp[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: 0.141 (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)
 

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