7.12.8 problem 9

Internal problem ID [390]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.6 (Forced oscillations and resonance). Problems at page 171
Problem number : 9
Date solved : Wednesday, February 05, 2025 at 03:31:29 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 37

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

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

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 55

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

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