75.1.7 problem 8

Internal problem ID [16591]
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 : Thursday, March 13, 2025 at 08:25:16 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

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

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

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

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

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

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

✓ Sympy. Time used: 0.870 (sec). Leaf size: 17

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

\[ y{\left (x \right )} = e^{C_{1} + W\left (\left (- x - 1\right ) e^{- C_{1}}\right )} - 1 \]