81.1.29 problem 2-27

Internal problem ID [21474]
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 : 2-27
Date solved : Thursday, October 02, 2025 at 07:39:20 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 2 x -6 y+3-\left (1+x -3 y\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.018 (sec). Leaf size: 21

ode:=2*x-6*y(x)+3-(x-3*y(x)+1)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {x}{3}+\frac {\operatorname {LambertW}\left (\frac {c_1 \,{\mathrm e}^{-\frac {8}{3}+\frac {25 x}{3}}}{3}\right )}{5}+\frac {8}{15} \]

✓ Mathematica. Time used: 2.54 (sec). Leaf size: 43

ode=(2*x-6*y[x]+3)-(x-3*y[x]+1)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{15} \left (3 W\left (-e^{\frac {25 x}{3}-1+c_1}\right )+5 x+8\right )\\ y(x)&\to \frac {1}{15} (5 x+8) \end{align*}

✓ Sympy. Time used: 2.231 (sec). Leaf size: 105

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x - (x - 3*y(x) + 1)*Derivative(y(x), x) - 6*y(x) + 3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = \frac {x}{3} + \frac {W\left (- \frac {\sqrt [3]{C_{1} e^{25 x}}}{3 e^{\frac {8}{3}}}\right )}{5} + \frac {8}{15}, \ y{\left (x \right )} = \frac {x}{3} + \frac {W\left (\frac {\sqrt [3]{C_{1} e^{25 x}} \left (1 - \sqrt {3} i\right )}{6 e^{\frac {8}{3}}}\right )}{5} + \frac {8}{15}, \ y{\left (x \right )} = \frac {x}{3} + \frac {W\left (\frac {\sqrt [3]{C_{1} e^{25 x}} \left (1 + \sqrt {3} i\right )}{6 e^{\frac {8}{3}}}\right )}{5} + \frac {8}{15}\right ] \]