90.15.10 problem 11

Internal problem ID [25257]
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 : 11
Date solved : Thursday, October 02, 2025 at 11:59:24 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=\cos \left (t \right ) \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) = cos(t); 
dsolve(ode,y(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.039 (sec). Leaf size: 25

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

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

✓ Sympy. Time used: 0.048 (sec). Leaf size: 31

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(y(t) - cos(t) + 3*Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} \sin {\left (\frac {\sqrt {3} t}{3} \right )} + C_{2} \cos {\left (\frac {\sqrt {3} t}{3} \right )} - \frac {\cos {\left (t \right )}}{2} \]