62.11.2 problem Ex 2

Internal problem ID [12773]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter 2, differential equations of the first order and the first degree. Article 18. Transformation of variables. Page 26
Problem number : Ex 2
Date solved : Monday, March 31, 2025 at 07:04:21 AM
CAS classification : [[_homogeneous, `class C`], [_Abel, `2nd type`, `class C`], _dAlembert]

\begin{align*} \left (x +y\right ) y^{\prime }-1&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 21

ode:=(x+y(x))*diff(y(x),x)-1 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\operatorname {LambertW}\left (-c_1 \,{\mathrm e}^{-x -1}\right )-x -1 \]

✓ Mathematica. Time used: 0.072 (sec). Leaf size: 35

ode=(x+y[x])*D[y[x],x]-1==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [x=e^{y(x)} \int _1^{y(x)}e^{-K[1]} K[1]dK[1]+c_1 e^{y(x)},y(x)\right ] \]

✓ Sympy. Time used: 0.557 (sec). Leaf size: 17

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

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