79.8.1 problem (a)

Internal problem ID [21105]
Book : Ordinary Differential Equations. By Wolfgang Walter. Graduate texts in Mathematics. Springer. NY. QA372.W224 1998
Section : Chapter 2. Theory of First order differential equations. Excercises XII at page 98
Problem number : (a)
Date solved : Thursday, October 02, 2025 at 07:08:23 PM
CAS classification : [_Abel]

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \\ \end{align*}

✗ Maple

ode:=diff(y(x),x) = x^3+y(x)^3; 
ic:=[y(0) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[y[x],x]==x^3+y[x]^3; 
ic={y[0]==1}; 
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 = {y(0): 1} 
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