13.3.1 problem 9

Internal problem ID [3544]
Book : Differential equations and linear algebra, Stephen W. Goode, second edition, 2000
Section : 1.8, page 68
Problem number : 9
Date solved : Tuesday, September 30, 2025 at 06:42:01 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (3 x -y\right ) y^{\prime }&=3 y \end{align*}

✓ Maple. Time used: 0.012 (sec). Leaf size: 17

ode:=(3*x-y(x))*diff(y(x),x) = 3*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {3 x}{\operatorname {LambertW}\left (-3 x \,{\mathrm e}^{-3 c_1}\right )} \]

✓ Mathematica. Time used: 3.789 (sec). Leaf size: 25

ode=(3*x-y[x])*D[y[x],x]==3*y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {3 x}{W\left (-3 e^{-c_1} x\right )}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.373 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((3*x - y(x))*Derivative(y(x), x) - 3*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = e^{C_{1} + W\left (- 3 x e^{- C_{1}}\right )} \]