Internal problem ID [212]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.4, Mechanical Vibrations. Page 337
Problem number: 15.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {\frac {x^{\prime \prime }}{2}+3 x^{\prime }+4 x=0} \end {gather*} With initial conditions \begin {align*} [x \relax (0) = 2, x^{\prime }\relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.01 (sec). Leaf size: 17
dsolve([1/2*diff(x(t),t$2)+3*diff(x(t),t)+4*x(t)=0,x(0) = 2, D(x)(0) = 0],x(t), singsol=all)
\[ x \relax (t ) = -2 \,{\mathrm e}^{-4 t}+4 \,{\mathrm e}^{-2 t} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 20
DSolve[{1/2*x''[t]+3*x'[t]+4*x[t]==0,{x[0]==2,x'[0]==0}},x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^{-4 t} \left (4 e^{2 t}-2\right ) \\ \end{align*}