50.9.24 problem 2(f)

Internal problem ID [7960]
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 : 2(f)
Date solved : Monday, January 27, 2025 at 03:34:06 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+8 y^{\prime }-9 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=2\\ y^{\prime }\left (1\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.034 (sec). Leaf size: 19

dsolve([diff(y(x),x$2)+8*diff(y(x),x)-9*y(x)=0,y(1) = 2, D(y)(1) = 0],y(x), singsol=all)
 

\[ y = \frac {9 \,{\mathrm e}^{x -1}}{5}+\frac {{\mathrm e}^{9-9 x}}{5} \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 26

DSolve[{D[y[x],{x,2}]+8*D[y[x],x]-9*y[x]==0,{y[1]==2,Derivative[1][y][1]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{5} e^{9-9 x}+\frac {9 e^{x-1}}{5} \]