85.21.7 problem 1 (g)

Internal problem ID [22570]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. A Exercises at page 55
Problem number : 1 (g)
Date solved : Thursday, October 02, 2025 at 08:51:50 PM
CAS classification : [[_homogeneous, `class C`], [_Abel, `2nd type`, `class C`], _dAlembert]

\begin{align*} y^{\prime }&=\frac {1}{x -3 y} \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 21

ode:=diff(y(x),x) = 1/(x-3*y(x)); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\operatorname {LambertW}\left (\frac {c_1 \,{\mathrm e}^{\frac {x}{3}-1}}{3}\right )+\frac {x}{3}-1 \]

✓ Mathematica. Time used: 60.019 (sec). Leaf size: 30

ode=D[y[x],x] == 1/(x-3*y[x]); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{3} \left (-3 W\left (\frac {1}{3} c_1 e^{\frac {x}{3}-1}\right )+x-3\right ) \end{align*}

✓ Sympy. Time used: 0.835 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - 1/(x - 3*y(x)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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