79.1.5 problem (e)

Internal problem ID [21082]
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 : (e)
Date solved : Thursday, October 02, 2025 at 07:06:50 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.466 (sec). Leaf size: 29

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

\[ y = \frac {-\operatorname {RootOf}\left (-2 c_1 \,\textit {\_Z}^{3} x +\textit {\_Z}^{4}-1\right )+\left (x -1\right ) c_1}{c_1} \]

✓ Mathematica. Time used: 60.121 (sec). Leaf size: 2637

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

Too large to display

✓ Sympy. Time used: 48.169 (sec). Leaf size: 1122

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

\[ \text {Solution too large to show} \]