85.56.10 problem 2 (d)

Internal problem ID [22835]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 4. Linear differential equations. A Exercises at page 199
Problem number : 2 (d)
Date solved : Thursday, October 02, 2025 at 09:15:33 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 28

ode:=diff(diff(q(t),t),t)+q(t) = t*sin(t)+cos(t); 
dsolve(ode,q(t), singsol=all);
 

\[ q = \frac {\left (-t^{2}+4 c_1 +2\right ) \cos \left (t \right )}{4}+\frac {3 \left (t +\frac {4 c_2}{3}\right ) \sin \left (t \right )}{4} \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 27

ode=D[q[t],{t,2}]+q[t]==t*sin(t)+cos(t); 
ic={}; 
DSolve[{ode,ic},q[t],t,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.095 (sec). Leaf size: 22

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

\[ q{\left (t \right )} = \left (C_{1} - \frac {t^{2}}{4}\right ) \cos {\left (t \right )} + \left (C_{2} + \frac {3 t}{4}\right ) \sin {\left (t \right )} \]