20.1.9 problem 5.b

Internal problem ID [4249]
Book : Differential equations with applications and historial notes, George F. Simmons. Second edition. 1971
Section : Chapter 2, section 7, page 37
Problem number : 5.b
Date solved : Tuesday, September 30, 2025 at 07:08:51 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {x +y+4}{x +y-6} \end{align*}

✓ Maple. Time used: 0.019 (sec). Leaf size: 21

ode:=diff(y(x),x) = (x+y(x)+4)/(x+y(x)-6); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 2.296 (sec). Leaf size: 35

ode=D[y[x],x]==(x+y[x]+4)/(x+y[x]-6); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -5 W\left (-e^{-\frac {2 x}{5}-1+c_1}\right )-x+1\\ y(x)&\to 1-x \end{align*}

✓ Sympy. Time used: 5.125 (sec). Leaf size: 228

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - (x + y(x) + 4)/(x + y(x) - 6),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - x - 5 W\left (\frac {\sqrt [5]{C_{1} e^{- 2 x}} e^{\frac {1}{5}}}{10}\right ) + 1, \ y{\left (x \right )} = - x - 5 W\left (\frac {\sqrt [5]{C_{1} e^{- 2 x}} \left (-1 + \sqrt {5} + \sqrt {2} i \sqrt {\sqrt {5} + 5}\right ) e^{\frac {1}{5}}}{40}\right ) + 1, \ y{\left (x \right )} = - x - 5 W\left (- \frac {\sqrt [5]{C_{1} e^{- 2 x}} \left (1 + \sqrt {5} - \sqrt {2} i \sqrt {5 - \sqrt {5}}\right ) e^{\frac {1}{5}}}{40}\right ) + 1, \ y{\left (x \right )} = - x - 5 W\left (- \frac {\sqrt [5]{C_{1} e^{- 2 x}} \left (1 + \sqrt {5} + \sqrt {2} i \sqrt {5 - \sqrt {5}}\right ) e^{\frac {1}{5}}}{40}\right ) + 1, \ y{\left (x \right )} = - x - 5 W\left (- \frac {\sqrt [5]{C_{1} e^{- 2 x}} \left (- \sqrt {5} + 1 + \sqrt {2} i \sqrt {\sqrt {5} + 5}\right ) e^{\frac {1}{5}}}{40}\right ) + 1\right ] \]