Internal problem ID [10334]
Book: A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY.
2015.
Section: Chapter 1, First order differential equations. Section 1.1 First order equations. Exercises page
10
Problem number: 4.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {x^{\prime \prime }+2 x^{\prime }+2 x=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
dsolve(diff(x(t),t$2)+2*diff(x(t),t)+2*x(t)=0,x(t), singsol=all)
\[ x \left (t \right ) = c_{1} {\mathrm e}^{-t} \sin \left (t \right )+c_{2} {\mathrm e}^{-t} \cos \left (t \right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 22
DSolve[x''[t]+2*x'[t]+2*x[t]==0,x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^{-t} (c_2 \cos (t)+c_1 \sin (t)) \\ \end{align*}