68.11.7 problem 19

Internal problem ID [17544]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.3, page 156
Problem number : 19
Date solved : Thursday, October 02, 2025 at 02:25:16 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 19

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

\[ y = \sin \left (t \right ) c_2 +\cos \left (t \right ) c_1 -\frac {\cos \left (2 t \right )}{3} \]

✓ Mathematica. Time used: 0.023 (sec). Leaf size: 52

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

\begin{align*} y(t)&\to \sin (t) \int _1^t\cos (K[1]) \cos (2 K[1])dK[1]-\frac {1}{2} \cos ^2(t)+\cos (t) \left (\frac {1}{6} \cos (3 t)+c_1\right )+c_2 \sin (t) \end{align*}

✓ Sympy. Time used: 0.035 (sec). Leaf size: 19

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

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