80.3.22 problem 23

Internal problem ID [21186]
Book : A Textbook on Ordinary Differential Equations by Shair Ahmad and Antonio Ambrosetti. Second edition. ISBN 978-3-319-16407-6. Springer 2015
Section : Chapter 3. First order nonlinear differential equations. Excercise 3.7 at page 67
Problem number : 23
Date solved : Thursday, October 02, 2025 at 07:16:10 PM
CAS classification : [_exact, _rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class A`]]

\begin{align*} y-x^{{1}/{3}}+\left (x +y\right ) y^{\prime }&=0 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.049 (sec). Leaf size: 24

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

\[ y = -x +\frac {\sqrt {4 x^{2}+6 x^{{4}/{3}}+4}}{2} \]

✓ Mathematica. Time used: 6.446 (sec). Leaf size: 27

ode=(y[x]-x^(1/3))+(x+y[x])*D[y[x],x]==0; 
ic={y[0]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \sqrt {\frac {3 x^{4/3}}{2}+x^2+1}-x \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**(1/3) + (x + y(x))*Derivative(y(x), x) + y(x),0) 
ics = {y(0): 1} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -(x**(1/3) - y(x))/(x + y(x)) + Derivative(y(x), x) cannot be solved by the factorable group method