74.1.43 problem 50

Internal problem ID [15823]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 1. Introduction to Differential Equations. Exercises 1.1, page 10
Problem number : 50
Date solved : Tuesday, January 28, 2025 at 08:08:15 AM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 12

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

\[ y = \frac {17}{9}+\frac {{\mathrm e}^{-9 x}}{9} \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 16

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

\[ y(x)\to \frac {1}{9} \left (e^{-9 x}+17\right ) \]