Internal problem ID [5532]
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(q).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+4 y^{\prime }+5 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 21
dsolve(diff(y(x),x$2)+4*diff(y(x),x)+5*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{-2 x} \sin \relax (x )+c_{2} {\mathrm e}^{-2 x} \cos \relax (x ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 22
DSolve[y''[x]+4*y'[x]+5*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-2 x} (c_2 \cos (x)+c_1 \sin (x)) \\ \end{align*}