39.5.16 problem Problem 24.46

Internal problem ID [6558]
Book : Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill 2014
Section : Chapter 24. Solutions of linear DE by Laplace transforms. Supplementary Problems. page 248
Problem number : Problem 24.46
Date solved : Monday, January 27, 2025 at 02:12:14 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} q^{\prime \prime }+9 q^{\prime }+14 q&=\frac {\sin \left (t \right )}{2} \end{align*}

Using Laplace method With initial conditions

\begin{align*} q \left (0\right )&=0\\ q^{\prime }\left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.186 (sec). Leaf size: 25

dsolve([diff(q(t),t$2)+9*diff(q(t),t)+14*q(t)=1/2*sin(t),q(0) = 0, D(q)(0) = 1],q(t), singsol=all)
 

\[ q = \frac {11 \,{\mathrm e}^{-2 t}}{50}-\frac {9 \cos \left (t \right )}{500}+\frac {13 \sin \left (t \right )}{500}-\frac {101 \,{\mathrm e}^{-7 t}}{500} \]

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 32

DSolve[{D[ q[t],{t,2}]+9*D[ q[t],t]+14*q[t]==1/2*Sin[t],{q[0]==0,Derivative[1][q][0]==1}},q[t],t,IncludeSingularSolutions -> True]
 

\[ q(t)\to \frac {1}{500} \left (-101 e^{-7 t}+110 e^{-2 t}+13 \sin (t)-9 \cos (t)\right ) \]