78.6.16 problem 4 (c)

Internal problem ID [18113]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Section 10 (Linear equations). Problems at page 82
Problem number : 4 (c)
Date solved : Monday, March 31, 2025 at 05:11:58 PM
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: 0.007 (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: 0.063 (sec). Leaf size: 18

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

\[ \text {Solve}\left [x=e^{y(x)} y(x)+c_1 y(x),y(x)\right ] \]

✓ Sympy. Time used: 1.154 (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)
 

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