90.14.10 problem 19

Internal problem ID [25238]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 3. Second Order Constant Coefficient Linear Differential Equations. Exercises at page 243
Problem number : 19
Date solved : Thursday, October 02, 2025 at 11:59:13 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 19

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

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

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 27

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

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

✓ Sympy. Time used: 0.133 (sec). Leaf size: 15

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

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