90.25.3 problem 3

Internal problem ID [25384]
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 : 3
Date solved : Friday, October 03, 2025 at 12:00:47 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&={\mathrm e}^{t} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 21

ode:=diff(diff(y(t),t),t)-2*diff(y(t),t)+5*y(t) = exp(t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = {\mathrm e}^{t} \left (\frac {1}{4}+c_2 \sin \left (2 t \right )+c_1 \cos \left (2 t \right )\right ) \]

✓ Mathematica. Time used: 0.033 (sec). Leaf size: 33

ode=D[y[t],{t,2}]-2*D[y[t],t]+5*y[t]==Exp[t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {1}{4} e^t ((1+4 c_2) \cos (2 t)+4 c_1 \sin (2 t)+1) \end{align*}

✓ Sympy. Time used: 0.130 (sec). Leaf size: 22

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(5*y(t) - exp(t) - 2*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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