26.3.7 problem Exact Differential equations. Exercise 9.10, page 79

Internal problem ID [6940]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 9
Problem number : Exact Differential equations. Exercise 9.10, page 79
Date solved : Tuesday, September 30, 2025 at 04:07:03 PM
CAS classification : [_exact]

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

✓ Maple. Time used: 0.007 (sec). Leaf size: 26

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

\[ \frac {x^{3}}{3}+x y^{2}-\frac {x^{2}}{2}-{\mathrm e}^{y}+c_1 = 0 \]

✓ Mathematica. Time used: 0.137 (sec). Leaf size: 32

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

\[ \text {Solve}\left [-\frac {x^3}{3}+\frac {x^2}{2}-x y(x)^2+e^{y(x)}=c_1,y(x)\right ] \]

✗ Sympy

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

NotImplementedError : The given ODE Derivative(y(x), x) - (-x**2 + x - y(x)**2)/(2*x*y(x) - exp(y(x))) cannot be solved by the factorable group method