32.4.14 problem Recognizable Exact Differential equations. Integrating factors. Exercise 10.6, page 90

Internal problem ID [5825]
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 10.6, page 90
Date solved : Tuesday, March 04, 2025 at 11:47:34 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational]

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

✓ Maple. Time used: 0.218 (sec). Leaf size: 28

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

\[ 2 y \left (x \right )+\ln \left (-x +y \left (x \right )\right )-\ln \left (x +y \left (x \right )\right )-2 x -c_{1} = 0 \]

✓ Mathematica. Time used: 0.347 (sec). Leaf size: 32

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

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

✓ Sympy. Time used: 36.175 (sec). Leaf size: 24

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

\[ C_{1} + x - y{\left (x \right )} - \frac {\log {\left (- x + y{\left (x \right )} \right )}}{2} + \frac {\log {\left (x + y{\left (x \right )} \right )}}{2} = 0 \]