Internal problem ID [14906]
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: 4.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {4 x^{\prime \prime }+2 x^{\prime }+8 x=0} \] With initial conditions \begin {align*} [x \left (0\right ) = 0, x^{\prime }\left (0\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 20
dsolve([4*diff(x(t),t$2)+2*diff(x(t),t)+8*x(t)=0,x(0) = 0, D(x)(0) = 2],x(t), singsol=all)
\[ x \left (t \right ) = \frac {8 \sqrt {31}\, {\mathrm e}^{-\frac {t}{4}} \sin \left (\frac {\sqrt {31}\, t}{4}\right )}{31} \]
✓ Solution by Mathematica
Time used: 0.025 (sec). Leaf size: 30
DSolve[{4*x''[t]+2*x'[t]+8*x[t]==0,{x[0]==0,x'[0]==2}},x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \frac {8 e^{-t/4} \sin \left (\frac {\sqrt {31} t}{4}\right )}{\sqrt {31}} \]