85.6.4 problem 4 (c)

Internal problem ID [22454]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 1. Differential equations in general. Section 1.3. C Exercises at page 22
Problem number : 4 (c)
Date solved : Thursday, October 02, 2025 at 08:39:45 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.037 (sec). Leaf size: 23

ode:=abs(diff(y(x),x))+abs(y(x)) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= 0 \\ y &= {\mathrm e}^{-x} c_1 \\ y &= \frac {{\mathrm e}^{x}}{c_1} \\ \end{align*}

✓ Mathematica. Time used: 0.211 (sec). Leaf size: 54

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

\begin{align*} y(x)&\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{| K[1]| }dK[1]\&\right ][-x+c_1]\\ y(x)&\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{| K[2]| }dK[2]\&\right ][x+c_1]\\ y(x)&\to 0 \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Abs(y(x)) + Abs(Derivative(y(x), x)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : solving Abs(Derivative(y(x), x)) when the argument is not real or imaginary.