1.6 problem Problem 12

Internal problem ID [2083]

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.
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 }+5 y=0} \end {gather*}

Solution by Maple

Time used: 0.002 (sec). Leaf size: 25

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

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

Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 26

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

\begin{align*} y(x)\to e^{-x} (c_2 \cos (2 x)+c_1 \sin (2 x)) \\ \end{align*}