76.13.41 problem 41

Internal problem ID [17623]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.3 (Linear homogeneous equations with constant coefficients). Problems at page 239
Problem number : 41
Date solved : Tuesday, January 28, 2025 at 10:45:50 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: 0.064 (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: 0.011 (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]
 

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