Internal problem ID [11444]
Book: A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag,
NY. 2015.
Section: Chapter 2, Second order linear equations. Section 2.2.3 Complex eigenvalues. Exercises
page 94
Problem number: 1(a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {x^{\prime \prime }+x^{\prime }+4 x=0} \] With initial conditions \begin {align*} [x \left (0\right ) = 1, x^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 31
dsolve([diff(x(t),t$2)+diff(x(t),t)+4*x(t)=0,x(0) = 1, D(x)(0) = 0],x(t), singsol=all)
\[ x \left (t \right ) = \frac {{\mathrm e}^{-\frac {t}{2}} \left (\sqrt {15}\, \sin \left (\frac {\sqrt {15}\, t}{2}\right )+15 \cos \left (\frac {\sqrt {15}\, t}{2}\right )\right )}{15} \]
✓ Solution by Mathematica
Time used: 0.044 (sec). Leaf size: 47
DSolve[{x''[t]+x'[t]+4*x[t]==0,{x[0]==1,x'[0]==0}},x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \frac {1}{15} e^{-t/2} \left (\sqrt {15} \sin \left (\frac {\sqrt {15} t}{2}\right )+15 \cos \left (\frac {\sqrt {15} t}{2}\right )\right ) \]