79.1.3 problem (c)

Internal problem ID [21080]
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 : (c)
Date solved : Thursday, October 02, 2025 at 07:06:04 PM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

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

✓ Maple. Time used: 0.040 (sec). Leaf size: 31

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

\[ y = 1+\left (-\ln \left (\frac {\left (x +2\right ) {\mathrm e}^{c_1 +1}+1}{x +2}\right )+c_1 \right ) \left (x +2\right ) \]

✓ Mathematica. Time used: 0.632 (sec). Leaf size: 41

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

\[ \text {Solve}\left [\frac {1-y(x)}{x+2}+\log \left (1-e^{\frac {y(x)+x+1}{x+2}}\right )+\log (x+2)=c_1,y(x)\right ] \]

✗ Sympy

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

TypeError : argument of type Mul is not iterable