35.4.10 problem 10

Internal problem ID [6128]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 4. OTHER METHODS FOR FIRST-ORDER EQUATIONS. page 406
Problem number : 10
Date solved : Sunday, March 30, 2025 at 10:40:36 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y^{2}-x y+\left (x^{2}+x y\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.011 (sec). Leaf size: 14

ode:=y(x)^2-x*y(x)+(x^2+x*y(x))*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {x}{\operatorname {LambertW}\left (c_1 \,x^{2}\right )} \]

✓ Mathematica. Time used: 4.162 (sec). Leaf size: 27

ode=(y[x]^2-x*y[x])+(x^2+x*y[x])*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \frac {x}{W\left (e^{-1-c_1} x^2\right )} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 1.120 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*y(x) + (x**2 + x*y(x))*Derivative(y(x), x) + y(x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {e^{C_{1} + W\left (x^{2} e^{- C_{1}}\right )}}{x} \]