90.25.2 problem 2

Internal problem ID [25383]
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 : 2
Date solved : Friday, October 03, 2025 at 12:00:46 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 22

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

\[ y = \frac {\left (t +4 c_2 \right ) {\mathrm e}^{2 t}}{4}+{\mathrm e}^{-2 t} c_1 \]

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 31

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

\begin{align*} y(t)&\to e^{2 t} \left (\frac {t}{4}-\frac {1}{16}+c_1\right )+c_2 e^{-2 t} \end{align*}

✓ Sympy. Time used: 0.075 (sec). Leaf size: 19

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

\[ y{\left (t \right )} = C_{2} e^{- 2 t} + \left (C_{1} + \frac {t}{4}\right ) e^{2 t} \]