8.12.9 problem 10

Internal problem ID [916]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.6, Forced Oscillations and Resonance. Page 362
Problem number : 10
Date solved : Tuesday, March 04, 2025 at 12:04:12 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{\prime \prime }+3 x^{\prime }+3 x&=8 \cos \left (10 t \right )+6 \sin \left (10 t \right ) \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 43

ode:=diff(diff(x(t),t),t)+3*diff(x(t),t)+3*x(t) = 8*cos(10*t)+6*sin(10*t); 
dsolve(ode,x(t), singsol=all);
 

\[ x \left (t \right ) = {\mathrm e}^{-\frac {3 t}{2}} \sin \left (\frac {\sqrt {3}\, t}{2}\right ) c_2 +{\mathrm e}^{-\frac {3 t}{2}} \cos \left (\frac {\sqrt {3}\, t}{2}\right ) c_1 -\frac {342 \sin \left (10 t \right )}{10309}-\frac {956 \cos \left (10 t \right )}{10309} \]

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 65

ode=D[x[t],{t,2}]+3*D[x[t],t]+3*x[t]==8*Cos[10*t]+6*Sin[10*t]; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\[ x(t)\to -\frac {2 (171 \sin (10 t)+478 \cos (10 t))}{10309}+c_2 e^{-3 t/2} \cos \left (\frac {\sqrt {3} t}{2}\right )+c_1 e^{-3 t/2} \sin \left (\frac {\sqrt {3} t}{2}\right ) \]

✓ Sympy. Time used: 0.282 (sec). Leaf size: 49

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(3*x(t) - 6*sin(10*t) - 8*cos(10*t) + 3*Derivative(x(t), t) + Derivative(x(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = \left (C_{1} \sin {\left (\frac {\sqrt {3} t}{2} \right )} + C_{2} \cos {\left (\frac {\sqrt {3} t}{2} \right )}\right ) e^{- \frac {3 t}{2}} - \frac {342 \sin {\left (10 t \right )}}{10309} - \frac {956 \cos {\left (10 t \right )}}{10309} \]