50.9.18 problem 1(r)

Internal problem ID [7954]
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(r)
Date solved : Monday, January 27, 2025 at 03:33:53 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+4 y^{\prime }-5 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 17

dsolve(diff(y(x),x$2)+4*diff(y(x),x)-5*y(x)=0,y(x), singsol=all)
 

\[ y = \left ({\mathrm e}^{6 x} c_{2} +c_{1} \right ) {\mathrm e}^{-5 x} \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 20

DSolve[D[y[x],{x,2}]+4*D[y[x],x]-5*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 e^{-5 x}+c_2 e^x \]