9.2 problem 1(b)

Internal problem ID [5517]

Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 2. Second-Order Linear Equations. Section 2.1. Linear Equations with Constant Coefficients. Page 62
Problem number: 1(b).
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _missing_x]]

Solve \begin {gather*} \boxed {y^{\prime \prime }+2 y^{\prime }+y=0} \end {gather*}

Solution by Maple

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

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

\[ y \relax (x ) = {\mathrm e}^{-x} c_{1}+c_{2} {\mathrm e}^{-x} x \]

Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 18

DSolve[y''[x]+2*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to e^{-x} (c_2 x+c_1) \\ \end{align*}