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 : Wednesday, February 05, 2025 at 04:46:07 AM
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*}

✓ Solution by Maple

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

dsolve(diff(x(t),t$2)+3*diff(x(t),t)+3*x(t)=8*cos(10*t)+6*sin(10*t),x(t), singsol=all)
 

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

✓ Solution by Mathematica

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

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

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