15.21.6 problem 28

Internal problem ID [3330]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 39, page 179
Problem number : 28
Date solved : Sunday, March 30, 2025 at 01:37:09 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

\begin{align*} y&=y^{\prime } x -{y^{\prime }}^{{2}/{3}} \end{align*}

✓ Maple. Time used: 0.054 (sec). Leaf size: 25

ode:=y(x) = x*diff(y(x),x)-diff(y(x),x)^(2/3); 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= -\frac {4}{27 x^{2}} \\ y &= 0 \\ y &= c_1 x -c_1^{{2}/{3}} \\ \end{align*}

✓ Mathematica. Time used: 0.066 (sec). Leaf size: 23

ode=y[x]==D[y[x],x]*x-D[y[x],x]^(2/3); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to c_1 x-c_1{}^{2/3} \\ y(x)\to 0 \\ \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)**(2/3),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out