90.14.3 problem 12

Internal problem ID [25231]
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 : 12
Date solved : Thursday, October 02, 2025 at 11:59:09 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 19

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

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

✓ Mathematica. Time used: 0.038 (sec). Leaf size: 26

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

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

✓ Sympy. Time used: 0.113 (sec). Leaf size: 15

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

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