80.8.9 problem 10

Internal problem ID [18509]
Book : Elementary Differential Equations. By Thornton C. Fry. D Van Nostrand. NY. First Edition (1929)
Section : Chapter VII. Linear equations of order higher than the first. section 56. Problems at page 163
Problem number : 10
Date solved : Thursday, March 13, 2025 at 12:11:19 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} 5 x^{\prime }+x&=\sin \left (3 t \right ) \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 23

ode:=5*diff(x(t),t)+x(t) = sin(3*t); 
dsolve(ode,x(t), singsol=all);
 

\[ x = -\frac {15 \cos \left (3 t \right )}{226}+\frac {\sin \left (3 t \right )}{226}+{\mathrm e}^{-\frac {t}{5}} c_{1} \]

✓ Mathematica. Time used: 0.08 (sec). Leaf size: 31

ode=5*D[x[t],t]+x[t]==Sin[3*t]; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\[ x(t)\to \frac {1}{226} (\sin (3 t)-15 \cos (3 t))+c_1 e^{-t/5} \]

✓ Sympy. Time used: 0.190 (sec). Leaf size: 24

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(x(t) - sin(3*t) + 5*Derivative(x(t), t),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = C_{1} e^{- \frac {t}{5}} + \frac {\sin {\left (3 t \right )}}{226} - \frac {15 \cos {\left (3 t \right )}}{226} \]