12.1.17 problem 9

Internal problem ID [1535]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 1, Introduction. Section 1.2 Page 14
Problem number : 9
Date solved : Saturday, March 29, 2025 at 10:58:00 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&={| y|}+1 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0 \end{align*}

✓ Maple. Time used: 0.182 (sec). Leaf size: 19

ode:=diff(y(x),x) = abs(y(x))+1; 
ic:=y(0) = 0; 
dsolve([ode,ic],y(x), singsol=all);
 

\begin{align*} y &= {\mathrm e}^{x}-1 \\ y &= 1-{\mathrm e}^{-x} \\ \end{align*}

✗ Mathematica

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

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✓ Sympy. Time used: 0.329 (sec). Leaf size: 22

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

\[ - \int \limits ^{y{\left (x \right )}} \frac {1}{\left |{y}\right | + 1}\, dy = - x - \int \limits ^{0} \frac {1}{\left |{y}\right | + 1}\, dy \]