50.3.23 problem 4(c)

Internal problem ID [7847]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.4 First Order Linear Equations. Page 15
Problem number : 4(c)
Date solved : Wednesday, March 05, 2025 at 05:08:25 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x)*G(y),0]`], [_Abel, `2nd type`, `class C`]]

\begin{align*} x y^{\prime }+2&=x^{3} \left (y-1\right ) y^{\prime } \end{align*}

✓ Maple. Time used: 0.012 (sec). Leaf size: 22

ode:=x*diff(y(x),x)+2 = x^3*(-1+y(x))*diff(y(x),x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {-\operatorname {LambertW}\left (c_{1} {\mathrm e}^{\frac {1}{x^{2}}}\right ) x^{2}+1}{x^{2}} \]

✓ Mathematica. Time used: 0.336 (sec). Leaf size: 33

ode=x*D[y[x],x]+2==x^3*(y[x]-1)*D[y[x],x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{x^2}-W\left (e^{\frac {1}{x^2}+\frac {1}{2} \left (-2-9 \sqrt [3]{-2} c_1\right )}\right ) \]

✓ Sympy. Time used: 1.343 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**3*(y(x) - 1)*Derivative(y(x), x) + x*Derivative(y(x), x) + 2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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