Internal problem ID [14940]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {y^{\prime }-\frac {y+1}{-y+x}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 34
dsolve(diff(y(x),x)=(y(x)+1)/(x-y(x)),y(x), singsol=all)
\[ y \left (x \right ) = \frac {-1-x -\operatorname {LambertW}\left (-\left (1+x \right ) {\mathrm e}^{-c_{1}}\right )}{\operatorname {LambertW}\left (-\left (1+x \right ) {\mathrm e}^{-c_{1}}\right )} \]
✓ Solution by Mathematica
Time used: 0.132 (sec). Leaf size: 34
DSolve[y'[x]==(y[x]+1)/(x-y[x]),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [x=(y(x)+1) \left (-\frac {1}{y(x)+1}-\log (y(x)+1)\right )+c_1 (y(x)+1),y(x)\right ] \]