79.1.2 problem (b)

Internal problem ID [21079]
Book : Ordinary Differential Equations. By Wolfgang Walter. Graduate texts in Mathematics. Springer. NY. QA372.W224 1998
Section : Chapter 1. First order equations: Some integrable cases. Excercises XII at page 23
Problem number : (b)
Date solved : Thursday, October 02, 2025 at 07:05:59 PM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

\begin{align*} y^{\prime }&=\frac {1+y}{x +2}+{\mathrm e}^{\frac {1+y}{x +2}} \end{align*}

✓ Maple. Time used: 0.008 (sec). Leaf size: 23

ode:=diff(y(x),x) = (1+y(x))/(x+2)+exp((1+y(x))/(x+2)); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -1+\left (-x -2\right ) \ln \left (-\ln \left (x +2\right )-c_1 \right ) \]

✓ Mathematica. Time used: 0.761 (sec). Leaf size: 22

ode=D[y[x],x]==(y[x]+1)/(x+2)+Exp[(y[x]+1)/(x+2)]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -1-((x+2) \log (-\log (x+2)+c_1)) \end{align*}

✗ Sympy

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

TypeError : argument of type Mul is not iterable