26.2.2 problem Differential equations with Linear Coefficients. Exercise 8.2, page 69

Internal problem ID [6921]
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 8.2, page 69
Date solved : Tuesday, September 30, 2025 at 04:05:48 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.021 (sec). Leaf size: 21

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

\[ y = -\frac {3 x}{2}-\frac {2 \operatorname {LambertW}\left (-\frac {c_1 \,{\mathrm e}^{\frac {1}{4}-\frac {25 x}{4}}}{4}\right )}{5}+\frac {1}{10} \]

✓ Mathematica. Time used: 2.43 (sec). Leaf size: 43

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

\begin{align*} y(x)&\to \frac {1}{10} \left (-4 W\left (-e^{-\frac {25 x}{4}-1+c_1}\right )-15 x+1\right )\\ y(x)&\to \frac {1}{10}-\frac {3 x}{2} \end{align*}

✓ Sympy. Time used: 2.677 (sec). Leaf size: 136

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

\[ \left [ y{\left (x \right )} = - \frac {3 x}{2} - \frac {2 W\left (- \frac {\sqrt [4]{C_{1} e^{- 25 x}} e^{\frac {1}{4}}}{4}\right )}{5} + \frac {1}{10}, \ y{\left (x \right )} = - \frac {3 x}{2} - \frac {2 W\left (\frac {\sqrt [4]{C_{1} e^{- 25 x}} e^{\frac {1}{4}}}{4}\right )}{5} + \frac {1}{10}, \ y{\left (x \right )} = - \frac {3 x}{2} - \frac {2 W\left (- \frac {i \sqrt [4]{C_{1} e^{- 25 x}} e^{\frac {1}{4}}}{4}\right )}{5} + \frac {1}{10}, \ y{\left (x \right )} = - \frac {3 x}{2} - \frac {2 W\left (\frac {i \sqrt [4]{C_{1} e^{- 25 x}} e^{\frac {1}{4}}}{4}\right )}{5} + \frac {1}{10}\right ] \]