7.8.7 problem 7

Internal problem ID [221]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.1 (Introduction. Second order linear equations). Problems at page 111
Problem number : 7
Date solved : Tuesday, March 04, 2025 at 11:05:26 AM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=-2\\ y^{\prime }\left (0\right )&=8 \end{align*}

✓ Maple. Time used: 0.010 (sec). Leaf size: 12

ode:=diff(diff(y(x),x),x)+diff(y(x),x) = 0; 
ic:=y(0) = -2, D(y)(0) = 8; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = 6-8 \,{\mathrm e}^{-x} \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 14

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

\[ y(x)\to 6-8 e^{-x} \]

✓ Sympy. Time used: 0.126 (sec). Leaf size: 8

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): -2, Subs(Derivative(y(x), x), x, 0): 8} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 6 - 8 e^{- x} \]