Internal problem ID [10432]
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 2.2.4. Applications. Exercises page
99
Problem number: 1.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {x^{\prime \prime }+x^{\prime }+x=0} \] With initial conditions \begin {align*} [x \left (0\right ) = 1, x^{\prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 28
dsolve([diff(x(t),t$2)+diff(x(t),t)+x(t)=0,x(0) = 1, D(x)(0) = 1],x(t), singsol=all)
\[ x \left (t \right ) = {\mathrm e}^{-\frac {t}{2}} \left (\sqrt {3}\, \sin \left (\frac {\sqrt {3}\, t}{2}\right )+\cos \left (\frac {\sqrt {3}\, t}{2}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 42
DSolve[{x''[t]+x'[t]+x[t]==0,{x[0]==1,x'[0]==1}},x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^{-t/2} \left (\sqrt {3} \sin \left (\frac {\sqrt {3} t}{2}\right )+\cos \left (\frac {\sqrt {3} t}{2}\right )\right ) \\ \end{align*}