68.4.63 problem 60 (b)

Internal problem ID [17243]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number : 60 (b)
Date solved : Thursday, October 02, 2025 at 01:59:44 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.019 (sec). Leaf size: 19

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

\[ y = x -\frac {5 \operatorname {LambertW}\left (-\frac {2 c_1 \,{\mathrm e}^{-\frac {6}{5}+\frac {x}{5}}}{5}\right )}{2}-3 \]

✓ Mathematica. Time used: 2.2 (sec). Leaf size: 33

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

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

✓ Sympy. Time used: 7.477 (sec). Leaf size: 230

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

\[ \left [ y{\left (x \right )} = x - \frac {5 W\left (\frac {2 \sqrt [5]{C_{1} e^{x}}}{5 e^{\frac {6}{5}}}\right )}{2} - 3, \ y{\left (x \right )} = x - \frac {5 W\left (\frac {\sqrt [5]{C_{1} e^{x}} \left (-1 + \sqrt {5} + \sqrt {2} i \sqrt {\sqrt {5} + 5}\right )}{10 e^{\frac {6}{5}}}\right )}{2} - 3, \ y{\left (x \right )} = x - \frac {5 W\left (- \frac {\sqrt [5]{C_{1} e^{x}} \left (1 + \sqrt {5} - \sqrt {2} i \sqrt {5 - \sqrt {5}}\right )}{10 e^{\frac {6}{5}}}\right )}{2} - 3, \ y{\left (x \right )} = x - \frac {5 W\left (- \frac {\sqrt [5]{C_{1} e^{x}} \left (1 + \sqrt {5} + \sqrt {2} i \sqrt {5 - \sqrt {5}}\right )}{10 e^{\frac {6}{5}}}\right )}{2} - 3, \ y{\left (x \right )} = x - \frac {5 W\left (- \frac {\sqrt [5]{C_{1} e^{x}} \left (- \sqrt {5} + 1 + \sqrt {2} i \sqrt {\sqrt {5} + 5}\right )}{10 e^{\frac {6}{5}}}\right )}{2} - 3\right ] \]