Internal problem ID [4707]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {q^{\prime \prime }+9 q^{\prime }+14 q-\frac {\sin \relax (t )}{2}=0} \end {gather*} With initial conditions \begin {align*} [q \relax (0) = 0, q^{\prime }\relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.012 (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)
\[ q \relax (t ) = \frac {11 \,{\mathrm e}^{-2 t}}{50}-\frac {101 \,{\mathrm e}^{-7 t}}{500}-\frac {9 \cos \relax (t )}{500}+\frac {13 \sin \relax (t )}{500} \]
✓ Solution by Mathematica
Time used: 0.032 (sec). Leaf size: 32
DSolve[{q''[t]+9*q'[t]+14*q[t]==1/2*Sin[t],{q[0]==0,q'[0]==1}},q[t],t,IncludeSingularSolutions -> True]
\begin{align*} q(t)\to \frac {1}{500} \left (-101 e^{-7 t}+110 e^{-2 t}+13 \sin (t)-9 \cos (t)\right ) \\ \end{align*}