68.12.21 problem 21

Internal problem ID [17615]
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 : 21
Date solved : Thursday, October 02, 2025 at 02:26:18 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=\frac {{\mathrm e}^{2 t}}{t^{2}} \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 19

ode:=diff(diff(y(t),t),t)-4*diff(y(t),t)+4*y(t) = 1/t^2*exp(2*t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = {\mathrm e}^{2 t} \left (t c_1 -\ln \left (t \right )+c_2 -1\right ) \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 23

ode=D[y[t],{t,2}]-4*D[y[t],t]+4*y[t]==1/t^2*Exp[2*t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to e^{2 t} (-\log (t)+c_2 t-1+c_1) \end{align*}

✓ Sympy. Time used: 0.170 (sec). Leaf size: 15

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(4*y(t) - 4*Derivative(y(t), t) + Derivative(y(t), (t, 2)) - exp(2*t)/t**2,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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