90.12.9 problem 9

Internal problem ID [25211]
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 213
Problem number : 9
Date solved : Thursday, October 02, 2025 at 11:58:59 PM
CAS classification : [[_2nd_order, _quadrature]]

\begin{align*} y^{\prime \prime }+2&=\cos \left (t \right ) \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 18

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

\[ y = -t^{2}-\cos \left (t \right )+c_1 t +c_2 \]

✓ Mathematica. Time used: 0.006 (sec). Leaf size: 21

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

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

✓ Sympy. Time used: 0.030 (sec). Leaf size: 14

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

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