30.11.12 problem 10 (c)

Internal problem ID [7592]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 4, Linear Second-Order Equations. EXERCISES 4.1 at page 156
Problem number : 10 (c)
Date solved : Tuesday, September 30, 2025 at 04:54:44 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+25 y&=\cos \left (\omega t \right ) \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 30

ode:=diff(diff(y(t),t),t)+25*y(t) = cos(omega*t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = \sin \left (5 t \right ) c_2 +\cos \left (5 t \right ) c_1 -\frac {\cos \left (\omega t \right )}{\omega ^{2}-25} \]

✓ Mathematica. Time used: 0.118 (sec). Leaf size: 33

ode=1*D[y[t],{t,2}]+0*D[y[t],t]+25*y[t]==Cos[\[Omega]*t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to -\frac {\cos (t \omega )}{\omega ^2-25}+c_1 \cos (5 t)+c_2 \sin (5 t) \end{align*}

✓ Sympy. Time used: 0.057 (sec). Leaf size: 26

from sympy import * 
t = symbols("t") 
w = symbols("w") 
y = Function("y") 
ode = Eq(25*y(t) - cos(t*w) + Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} \sin {\left (5 t \right )} + C_{2} \cos {\left (5 t \right )} - \frac {\cos {\left (t w \right )}}{w^{2} - 25} \]