Internal problem ID [14221]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {y^{\prime }-\frac {x -y+2}{2 x -2 y-1}=0} \]
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 19
dsolve(diff(y(x),x)=(x-y(x)+2)/(2*x-2*y(x)-1),y(x), singsol=all)
\[ y \left (x \right ) = x -\frac {5 \operatorname {LambertW}\left (-\frac {2 c_{1} {\mathrm e}^{\frac {x}{5}-\frac {6}{5}}}{5}\right )}{2}-3 \]
✓ Solution by Mathematica
Time used: 3.627 (sec). Leaf size: 33
DSolve[y'[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*}