22.1.3 problem 3

Internal problem ID [4089]
Book : Applied Differential equations, Newby Curle. Van Nostrand Reinhold. 1972
Section : Examples, page 35
Problem number : 3
Date solved : Tuesday, March 04, 2025 at 05:25:26 PM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

\begin{align*} y-x&={y^{\prime }}^{2} \left (1-\frac {2 y^{\prime }}{3}\right ) \end{align*}

✓ Maple. Time used: 0.034 (sec). Leaf size: 49

ode:=y(x)-x = diff(y(x),x)^2*(1-2/3*diff(y(x),x)); 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y \left (x \right ) &= x +\frac {1}{3} \\ y \left (x \right ) &= \frac {\left (2 x -2 c_{1} \right ) \sqrt {-x +c_{1}}}{3}+c_{1} \\ y \left (x \right ) &= \frac {\left (-2 x +2 c_{1} \right ) \sqrt {-x +c_{1}}}{3}+c_{1} \\ \end{align*}

✓ Mathematica. Time used: 176.55 (sec). Leaf size: 14234

ode=y[x]-x==D[y[x],x]^2*(1-2/3* D[y[x],x]); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x - (1 - 2*Derivative(y(x), x)/3)*Derivative(y(x), x)**2 + y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out