10.8.4 problem 10

Internal problem ID [1276]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Chapter 3, Second order linear equations, 3.3 Complex Roots of the Characteristic Equation , page 164
Problem number : 10
Date solved : Monday, January 27, 2025 at 04:49:25 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

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

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

\[ y = {\mathrm e}^{-x} \left (c_1 \sin \left (x \right )+c_2 \cos \left (x \right )\right ) \]

✓ Solution by Mathematica

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

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

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