22.1.48 problem 49

Internal problem ID [4354]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page 78
Problem number : 49
Date solved : Tuesday, September 30, 2025 at 07:23:07 AM
CAS classification : [_rational]

\begin{align*} x^{2}+y^{3}+y+\left (x^{3}+y^{2}-x \right ) y^{\prime }&=0 \end{align*}

✗ Maple

ode:=x^2+y(x)^3+y(x)+(x^3+y(x)^2-x)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=(x^2+y[x]^3+y[x])+( x^3+y[x]^2-x )*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2 + (x**3 - x + y(x)**2)*Derivative(y(x), x) + y(x)**3 + y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out