72.8.38 problem 38

Internal problem ID [19522]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Miscellaneous Problems for Chapter 2. Problems at page 99
Problem number : 38
Date solved : Thursday, October 02, 2025 at 04:38:48 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {-3 x -2 y-1}{2 x +3 y-1} \end{align*}

✓ Maple. Time used: 0.200 (sec). Leaf size: 31

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

\[ y = \frac {-2 c_1 x +c_1 -\sqrt {-5 \left (x +1\right )^{2} c_1^{2}+3}}{3 c_1} \]

✓ Mathematica. Time used: 0.091 (sec). Leaf size: 65

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

\begin{align*} y(x)&\to \frac {1}{3} \left (-\sqrt {-5 x^2-10 x+1+9 c_1}-2 x+1\right )\\ y(x)&\to \frac {1}{3} \left (\sqrt {-5 x^2-10 x+1+9 c_1}-2 x+1\right ) \end{align*}

✓ Sympy. Time used: 1.481 (sec). Leaf size: 51

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

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