90.15.4 problem 4

Internal problem ID [25251]
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 251
Problem number : 4
Date solved : Thursday, October 02, 2025 at 11:59:21 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=4 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 19

ode:=diff(diff(y(t),t),t)+3*diff(y(t),t)+2*y(t) = 4; 
dsolve(ode,y(t), singsol=all);
 

\[ y = -{\mathrm e}^{-2 t} c_1 +{\mathrm e}^{-t} c_2 +2 \]

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 23

ode=D[y[t],{t,2}]+3*D[y[t],{t,1}]+2*y[t]==4; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.053 (sec). Leaf size: 27

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

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