35.2.12 problem 12

Internal problem ID [6104]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 2. Separable equations. page 398
Problem number : 12
Date solved : Sunday, March 30, 2025 at 10:38:54 AM
CAS classification : [_separable]

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

With initial conditions

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

✓ Maple. Time used: 0.121 (sec). Leaf size: 11

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

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

✓ Mathematica. Time used: 1.976 (sec). Leaf size: 11

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

\[ y(x)\to W\left (\frac {e}{x}\right ) \]

✓ Sympy. Time used: 0.260 (sec). Leaf size: 8

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

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