20.1.6 problem Problem 12

Internal problem ID [3563]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.2, Basic Ideas and Terminology. page 21
Problem number : Problem 12
Date solved : Monday, January 27, 2025 at 07:44:06 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 22

dsolve(diff(y(x),x$2)+2*diff(y(x),x)+5*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 26

DSolve[D[y[x],{x,2}]+2*D[y[x],x]+5*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x} (c_2 \cos (2 x)+c_1 \sin (2 x)) \]