81.1.33 problem 2-31

Internal problem ID [21478]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 2. Separable differential equations
Problem number : 2-31
Date solved : Thursday, October 02, 2025 at 07:39:57 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} x +2 y-1+3 \left (x +2 y\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.021 (sec). Leaf size: 23

ode:=x+2*y(x)-1+3*(2*y(x)+x)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\operatorname {LambertW}\left (-{\mathrm e}^{-1-\frac {x}{6}+\frac {c_1}{6}}\right )-1-\frac {x}{2} \]

✓ Mathematica. Time used: 0.065 (sec). Leaf size: 75

ode=(x+2*y[x]-1)+3*(x+y[x])*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [2 \sqrt {13} \text {arctanh}\left (\frac {y(x)+3 x+2}{\sqrt {13} (y(x)+x)}\right )+78 c_1=13 \left (\log \left (\frac {-x^2-5 x y(x)-3 y(x)^2+y(x)+3 x+1}{(x+1)^2}\right )+2 \log (x+1)\right ),y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x + (3*x + 3*y(x))*Derivative(y(x), x) + 2*y(x) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out