32.4.12 problem Recognizable Exact Differential equations. Integrating factors. Exercise 10.4, page 90

Internal problem ID [5823]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 10
Problem number : Recognizable Exact Differential equations. Integrating factors. Exercise 10.4, page 90
Date solved : Sunday, March 30, 2025 at 10:18:50 AM
CAS classification : [_exact]

\begin{align*} x -2 x y+{\mathrm e}^{y}+\left (y-x^{2}+x \,{\mathrm e}^{y}\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.009 (sec). Leaf size: 28

ode:=x-2*x*y(x)+exp(y(x))+(y(x)-x^2+x*exp(y(x)))*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ -x^{2} y+x \,{\mathrm e}^{y}+\frac {x^{2}}{2}+\frac {y^{2}}{2}+c_1 = 0 \]

✓ Mathematica. Time used: 0.346 (sec). Leaf size: 35

ode=(x-2*x*y[x]+Exp[y[x]])+(y[x]-x^2+x*Exp[y[x]])*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [x^2 (-y(x))+\frac {x^2}{2}+x e^{y(x)}+\frac {y(x)^2}{2}=c_1,y(x)\right ] \]

✗ Sympy

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

Timed Out