74.4.63 problem 60 (b)

Internal problem ID [15956]
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 : Tuesday, January 28, 2025 at 08:24:38 AM
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*}

✓ Solution by Maple

Time used: 0.065 (sec). Leaf size: 19

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

\[ y = x -\frac {5 \operatorname {LambertW}\left (-\frac {2 c_{1} {\mathrm e}^{\frac {x}{5}-\frac {6}{5}}}{5}\right )}{2}-3 \]

✓ Solution by Mathematica

Time used: 3.216 (sec). Leaf size: 33

DSolve[D[y[x],x]==(x-y[x]+2)/(2*x-2*y[x]-1),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*}