90.25.1 problem 1

Internal problem ID [25382]
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 : 1
Date solved : Friday, October 03, 2025 at 12:00:46 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 25

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

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

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 22

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

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

✓ Sympy. Time used: 0.061 (sec). Leaf size: 15

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

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