44.5.14 problem 4(d)

Internal problem ID [9170]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.7. Homogeneous Equations. Page 28
Problem number : 4(d)
Date solved : Tuesday, September 30, 2025 at 06:11:29 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {x +y-1}{x +4 y+2} \end{align*}

✓ Maple. Time used: 0.581 (sec). Leaf size: 32

ode:=diff(y(x),x) = (x+y(x)-1)/(x+4*y(x)+2); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 60.189 (sec). Leaf size: 4611

ode=D[y[x],x]==(x+y[x]-1)/(x+4*y[x]+2); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-x - y(x) + 1)/(x + 4*y(x) + 2) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out