88.3.6 problem 6

Internal problem ID [23960]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 1. Introduction. Exercise at page 22
Problem number : 6
Date solved : Thursday, October 02, 2025 at 09:47:48 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (x +y+1\right ) y^{\prime }&=x +y+2 \end{align*}

✓ Maple. Time used: 0.014 (sec). Leaf size: 21

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

\[ y = -\frac {\operatorname {LambertW}\left (-{\mathrm e}^{-4 x} {\mathrm e}^{-3} c_1 \right )}{2}-x -\frac {3}{2} \]

✓ Mathematica. Time used: 2.295 (sec). Leaf size: 39

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

\begin{align*} y(x)&\to \frac {1}{2} \left (-W\left (-e^{-4 x-1+c_1}\right )-2 x-3\right )\\ y(x)&\to -x-\frac {3}{2} \end{align*}

✓ Sympy. Time used: 0.595 (sec). Leaf size: 22

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

\[ y{\left (x \right )} = - x - \frac {W\left (C_{1} e^{- 4 x - 3}\right )}{2} - \frac {3}{2} \]