Internal problem ID [218]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.4, Mechanical Vibrations. Page 337
Problem number: 21.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {x^{\prime \prime }+10 x^{\prime }+125 x=0} \end {gather*} With initial conditions \begin {align*} [x \relax (0) = 6, x^{\prime }\relax (0) = 50] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 23
dsolve([diff(x(t),t$2)+10*diff(x(t),t)+125*x(t)=0,x(0) = 6, D(x)(0) = 50],x(t), singsol=all)
\[ x \relax (t ) = 2 \,{\mathrm e}^{-5 t} \left (4 \sin \left (10 t \right )+3 \cos \left (10 t \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 24
DSolve[{x''[t]+10*x'[t]+125*x[t]==0,{x[0]==6,x'[0]==50}},x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^{-5 t} (8 \sin (10 t)+6 \cos (10 t)) \\ \end{align*}