26.2.11 problem Differential equations with Linear Coefficients. Exercise 8.11, page 69

Internal problem ID [6930]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 8
Problem number : Differential equations with Linear Coefficients. Exercise 8.11, page 69
Date solved : Tuesday, September 30, 2025 at 04:06:23 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} x +y+\left (3 x +3 y-4\right ) y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.354 (sec). Leaf size: 19

ode:=x+y(x)+(3*x+3*y(x)-4)*diff(y(x),x) = 0; 
ic:=[y(1) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {2 \operatorname {LambertW}\left (-1, -\frac {3 \,{\mathrm e}^{x -\frac {5}{2}}}{2}\right )}{3}-x +2 \]

✗ Mathematica

ode=(x+y[x])+(3*x+3*y[x]-4)*D[y[x],x]==0; 
ic=y[1]==0; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

{}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x + (3*x + 3*y(x) - 4)*Derivative(y(x), x) + y(x),0) 
ics = {y(1): 0} 
dsolve(ode,func=y(x),ics=ics)
 

ValueError : Couldnt solve for initial conditions