90.14.11 problem 20

Internal problem ID [25239]
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 : 20
Date solved : Thursday, October 02, 2025 at 11:59:14 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

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

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

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

✓ Mathematica. Time used: 0.033 (sec). Leaf size: 27

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

\begin{align*} y(t)&\to (-t+c_1) \cos (t)+\frac {1}{2} (1+2 c_2) \sin (t) \end{align*}

✓ Sympy. Time used: 0.055 (sec). Leaf size: 14

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

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