83.3.6 problem 2 (a)

Internal problem ID [21925]
Book : Differential Equations By Kaj L. Nielsen. Second edition 1966. Barnes and nobel. 66-28306
Section : Chapter III. First order differential equations of the first degree. Ex. IV at page 38
Problem number : 2 (a)
Date solved : Thursday, October 02, 2025 at 08:10:01 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.063 (sec). Leaf size: 10

ode:=(x+y(x))*diff(y(x),x) = y(x); 
ic:=[y(0) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {x}{\operatorname {LambertW}\left (x \right )} \]

✓ Mathematica. Time used: 2.644 (sec). Leaf size: 11

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

\begin{align*} y(x)&\to \frac {x}{W(x)} \end{align*}

✓ Sympy. Time used: 0.333 (sec). Leaf size: 7

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

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