86.7.10 problem 12

Internal problem ID [23157]
Book : An introduction to Differential Equations. By Howard Frederick Cleaves. 1969. Oliver and Boyd publisher. ISBN 0050015044
Section : Chapter 5. Linear equations of the second order with constant coefficients. Exercise 5c at page 83
Problem number : 12
Date solved : Thursday, October 02, 2025 at 09:23:35 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{\prime \prime }-9 x^{\prime }-10 x&=\cos \left (4 t \right ) \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 29

ode:=diff(diff(x(t),t),t)-9*diff(x(t),t)-10*x(t) = cos(4*t); 
dsolve(ode,x(t), singsol=all);
 

\[ x = {\mathrm e}^{-t} c_2 +{\mathrm e}^{10 t} c_1 -\frac {13 \cos \left (4 t \right )}{986}-\frac {9 \sin \left (4 t \right )}{493} \]

✓ Mathematica. Time used: 0.098 (sec). Leaf size: 38

ode=D[x[t],{t,2}]-9*D[x[t],t]-10*x[t]==Cos[4*t]; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to -\frac {9}{493} \sin (4 t)-\frac {13}{986} \cos (4 t)+c_1 e^{-t}+c_2 e^{10 t} \end{align*}

✓ Sympy. Time used: 0.164 (sec). Leaf size: 31

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(-10*x(t) - cos(4*t) - 9*Derivative(x(t), t) + Derivative(x(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = C_{1} e^{- t} + C_{2} e^{10 t} - \frac {9 \sin {\left (4 t \right )}}{493} - \frac {13 \cos {\left (4 t \right )}}{986} \]