75.1.7 problem 8

Internal problem ID [16670]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 1. Basic concepts and definitions. Exercises page 18
Problem number : 8
Date solved : Tuesday, January 28, 2025 at 09:17:31 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 34

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

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

✓ Solution by Mathematica

Time used: 0.107 (sec). Leaf size: 35

DSolve[D[y[x],x]==(y[x]+1)/(x-y[x]),y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [x=(y(x)+1) \left (\frac {y(x)}{y(x)+1}-\log (y(x)+1)\right )+c_1 (y(x)+1),y(x)\right ] \]