4.6.11 problem 11

Internal problem ID [1228]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Miscellaneous problems, end of chapter 2. Page 133
Problem number : 11
Date solved : Tuesday, September 30, 2025 at 04:30:12 AM
CAS classification : [_exact]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 39

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

\[ y = \frac {-x^{3}-3 x \operatorname {LambertW}\left (\frac {{\mathrm e}^{-\frac {x^{3}+3 c_1}{3 x}}}{x}\right )-3 c_1}{3 x} \]

✓ Mathematica. Time used: 2.951 (sec). Leaf size: 42

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

\begin{align*} y(x)&\to -W\left (\frac {e^{-\frac {x^2}{3}+\frac {c_1}{x}}}{x}\right )-\frac {x^2}{3}+\frac {c_1}{x} \end{align*}

✗ Sympy

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

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