32.2.1 problem 1

Internal problem ID [7718]
Book : Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY. 2001
Section : Program 24. First order differential equations. Further problems 24. page 1068
Problem number : 1
Date solved : Tuesday, September 30, 2025 at 05:01:59 PM
CAS classification : [_separable]

\begin{align*} x \left (y-3\right ) y^{\prime }&=4 y \end{align*}

✓ Maple. Time used: 0.008 (sec). Leaf size: 16

ode:=x*(y(x)-3)*diff(y(x),x) = 4*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -3 \operatorname {LambertW}\left (-\frac {{\mathrm e}^{-\frac {4 c_1}{3}}}{3 x^{{4}/{3}}}\right ) \]

✓ Mathematica. Time used: 10.016 (sec). Leaf size: 94

ode=x*(y[x]-3)*D[y[x],x]==4*y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -3 W\left (\frac {1}{3} \sqrt [3]{-\frac {e^{-c_1}}{x^4}}\right )\\ y(x)&\to -3 W\left (-\frac {1}{3} \sqrt [3]{-1} \sqrt [3]{-\frac {e^{-c_1}}{x^4}}\right )\\ y(x)&\to -3 W\left (\frac {1}{3} (-1)^{2/3} \sqrt [3]{-\frac {e^{-c_1}}{x^4}}\right )\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 1.179 (sec). Leaf size: 70

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*(y(x) - 3)*Derivative(y(x), x) - 4*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - 3 W\left (- \frac {\sqrt [3]{\frac {C_{1}}{x^{4}}}}{3}\right ), \ y{\left (x \right )} = - 3 W\left (\frac {\sqrt [3]{\frac {C_{1}}{x^{4}}} \left (1 - \sqrt {3} i\right )}{6}\right ), \ y{\left (x \right )} = - 3 W\left (\frac {\sqrt [3]{\frac {C_{1}}{x^{4}}} \left (1 + \sqrt {3} i\right )}{6}\right )\right ] \]