Internal problem ID [14907]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 5. Applications of Higher Order Equations. Exercises 5.2, page 241
Problem number: 5.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {x^{\prime \prime }+4 x^{\prime }+13 x=0} \] With initial conditions \begin {align*} [x \left (0\right ) = 1, x^{\prime }\left (0\right ) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 21
dsolve([diff(x(t),t$2)+4*diff(x(t),t)+13*x(t)=0,x(0) = 1, D(x)(0) = -1],x(t), singsol=all)
\[ x \left (t \right ) = \frac {{\mathrm e}^{-2 t} \left (\sin \left (3 t \right )+3 \cos \left (3 t \right )\right )}{3} \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 25
DSolve[{x''[t]+4*x'[t]+13*x[t]==0,{x[0]==1,x'[0]==-1}},x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \frac {1}{3} e^{-2 t} (\sin (3 t)+3 \cos (3 t)) \]