23.2.341 problem 388

Internal problem ID [5696]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 2. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF SECOND OR HIGHER DEGREE, page 278
Problem number : 388
Date solved : Tuesday, September 30, 2025 at 02:00:09 PM
CAS classification : [_Clairaut]

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

✓ Maple. Time used: 0.663 (sec). Leaf size: 17

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

\[ y = a \left (c_1^{3}+1\right )^{{1}/{3}}+c_1 x \]

✓ Mathematica. Time used: 0.095 (sec). Leaf size: 27

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

\begin{align*} y(x)&\to a \sqrt [3]{1+c_1{}^3}+c_1 x\\ y(x)&\to a \end{align*}

✗ Sympy

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

Timed Out