78.6.15 problem 4 (b)

Internal problem ID [18104]
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 (b)
Date solved : Thursday, March 13, 2025 at 11:37:04 AM
CAS classification : [[_1st_order, _with_linear_symmetries]]

\begin{align*} y-x y^{\prime }&=y^{\prime } y^{2} {\mathrm e}^{y} \end{align*}

✓ Maple. Time used: 0.013 (sec). Leaf size: 17

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

\[ -y \,{\mathrm e}^{y}-y c_1 +x = 0 \]

✓ Mathematica. Time used: 0.209 (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: 0.717 (sec). Leaf size: 12

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

\[ C_{1} + \frac {x}{y{\left (x \right )}} - e^{y{\left (x \right )}} = 0 \]