71.3.17 problem 12

Internal problem ID [14296]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.1, page 40
Problem number : 12
Date solved : Monday, March 31, 2025 at 12:15:59 PM
CAS classification : [_Abel]

\begin{align*} y^{\prime }&=x^{3}+y^{3} \end{align*}

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

NotImplementedError : The given ODE -x**3 - y(x)**3 + Derivative(y(x), x) cannot be solved by the lie group method