Internal problem ID [4706]
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 24.44.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {x^{\prime \prime }+4 x^{\prime }+4 x=0} \end {gather*} With initial conditions \begin {align*} [x \relax (0) = 2, x^{\prime }\relax (0) = -2] \end {align*}
✓ Solution by Maple
Time used: 0.008 (sec). Leaf size: 13
dsolve([diff(x(t),t$2)+4*diff(x(t),t)+4*x(t)=0,x(0) = 2, D(x)(0) = -2],x(t), singsol=all)
\[ x \relax (t ) = 2 \,{\mathrm e}^{-2 t} \left (t +1\right ) \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 47
DSolve[{x''[t]+3*x'[t]+4*x[t]==0,{x[0]==2,x'[0]==-2}},x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {2}{7} e^{-3 t/2} \left (\sqrt {7} \sin \left (\frac {\sqrt {7} t}{2}\right )+7 \cos \left (\frac {\sqrt {7} t}{2}\right )\right ) \\ \end{align*}