74.1.43 problem 50

Internal problem ID [15752]
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 : Monday, March 31, 2025 at 01:47:07 PM
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*}

✓ Maple. Time used: 0.040 (sec). Leaf size: 12

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

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

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

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

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

✓ Sympy. Time used: 0.170 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(9*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 2, Subs(Derivative(y(x), x), x, 0): -1} 
dsolve(ode,func=y(x),ics=ics)
 

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