78.8.38 problem 38

Internal problem ID [18157]
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, March 13, 2025 at 11:45:39 AM
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: 0.102 (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: 0.121 (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: 2.137 (sec). Leaf size: 51

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

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