74.22.15 problem 15

Internal problem ID [16583]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 6. Systems of Differential Equations. Exercises 6.1, page 282
Problem number : 15
Date solved : Thursday, March 13, 2025 at 08:23:47 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{\prime \prime }+16 x&=t \sin \left (t \right ) \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 26

ode:=diff(diff(x(t),t),t)+16*x(t) = t*sin(t); 
dsolve(ode,x(t), singsol=all);
 

\[ x \left (t \right ) = \sin \left (4 t \right ) c_{2} +\cos \left (4 t \right ) c_{1} -\frac {2 \cos \left (t \right )}{225}+\frac {t \sin \left (t \right )}{15} \]

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 33

ode=D[x[t],{t,2}]+16*x[t]==t*Sin[t]; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\[ x(t)\to \frac {1}{15} t \sin (t)-\frac {2 \cos (t)}{225}+c_1 \cos (4 t)+c_2 \sin (4 t) \]

✓ Sympy. Time used: 0.095 (sec). Leaf size: 29

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(-t*sin(t) + 16*x(t) + Derivative(x(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = C_{1} \sin {\left (4 t \right )} + C_{2} \cos {\left (4 t \right )} + \frac {t \sin {\left (t \right )}}{15} - \frac {2 \cos {\left (t \right )}}{225} \]