60.1.508 problem 521

Internal problem ID [10522]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 521
Date solved : Sunday, March 30, 2025 at 05:43:04 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

\begin{align*} {y^{\prime }}^{3}+x y^{\prime }-y&=0 \end{align*}

✓ Maple. Time used: 0.071 (sec). Leaf size: 37

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

\begin{align*} y &= \frac {2 \sqrt {3}\, \left (-x \right )^{{3}/{2}}}{9} \\ y &= -\frac {2 \sqrt {3}\, \left (-x \right )^{{3}/{2}}}{9} \\ y &= c_1 \left (c_1^{2}+x \right ) \\ \end{align*}

✓ Mathematica. Time used: 0.006 (sec). Leaf size: 54

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

\begin{align*} y(x)\to c_1 \left (x+c_1{}^2\right ) \\ y(x)\to -\frac {2 i x^{3/2}}{3 \sqrt {3}} \\ y(x)\to \frac {2 i x^{3/2}}{3 \sqrt {3}} \\ \end{align*}

✗ Sympy

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

Timed Out