10.7.15 problem 15

Internal problem ID [1263]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Chapter 3, Second order linear equations, 3.1 Homogeneous Equations with Constant Coefficients, page 144
Problem number : 15
Date solved : Monday, January 27, 2025 at 04:48:17 AM
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 )&=1\\ y^{\prime }\left (1\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.028 (sec). Leaf size: 19

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

\[ y = \frac {9 \,{\mathrm e}^{x -1}}{10}+\frac {{\mathrm e}^{9-9 x}}{10} \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 26

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

\[ y(x)\to \frac {1}{10} e^{9-9 x}+\frac {9 e^{x-1}}{10} \]