8.12.8 problem 9

Internal problem ID [915]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.6, Forced Oscillations and Resonance. Page 362
Problem number : 9
Date solved : Tuesday, March 04, 2025 at 12:03:37 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} 2 x^{\prime \prime }+2 x^{\prime }+x&=3 \sin \left (10 t \right ) \end{align*}

✓ Maple. Time used: 0.356 (sec). Leaf size: 37

ode:=2*diff(diff(x(t),t),t)+2*diff(x(t),t)+x(t) = 3*sin(10*t); 
dsolve(ode,x(t), singsol=all);
 

\[ x \left (t \right ) = {\mathrm e}^{-\frac {t}{2}} \sin \left (\frac {t}{2}\right ) c_2 +{\mathrm e}^{-\frac {t}{2}} \cos \left (\frac {t}{2}\right ) c_1 -\frac {597 \sin \left (10 t \right )}{40001}-\frac {60 \cos \left (10 t \right )}{40001} \]

✓ Mathematica. Time used: 0.023 (sec). Leaf size: 55

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

\[ x(t)\to -\frac {3 (199 \sin (10 t)+20 \cos (10 t))}{40001}+c_2 e^{-t/2} \cos \left (\frac {t}{2}\right )+c_1 e^{-t/2} \sin \left (\frac {t}{2}\right ) \]

✓ Sympy. Time used: 0.226 (sec). Leaf size: 37

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

\[ x{\left (t \right )} = \left (C_{1} \sin {\left (\frac {t}{2} \right )} + C_{2} \cos {\left (\frac {t}{2} \right )}\right ) e^{- \frac {t}{2}} - \frac {597 \sin {\left (10 t \right )}}{40001} - \frac {60 \cos {\left (10 t \right )}}{40001} \]