63.1.4 problem 4

Internal problem ID [13028]
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
Date solved : Tuesday, January 28, 2025 at 04:49:39 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} x^{\prime \prime }+2 x^{\prime }+2 x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 18

dsolve(diff(x(t),t$2)+2*diff(x(t),t)+2*x(t)=0,x(t), singsol=all)
 

\[ x \left (t \right ) = {\mathrm e}^{-t} \left (c_{2} \cos \left (t \right )+c_{1} \sin \left (t \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 22

DSolve[D[x[t],{t,2}]+2*D[x[t],t]+2*x[t]==0,x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to e^{-t} (c_2 \cos (t)+c_1 \sin (t)) \]