62.20.2 problem Ex 2

Internal problem ID [12845]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter V, Singular solutions. Article 33. Page 73
Problem number : Ex 2
Date solved : Monday, March 31, 2025 at 07:21:28 AM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

\begin{align*} 8 \left (1+y^{\prime }\right )^{3}&=27 \left (x +y\right ) \left (1-y^{\prime }\right )^{3} \end{align*}

✓ Maple. Time used: 0.158 (sec). Leaf size: 138

ode:=8*(1+diff(y(x),x))^3 = 27*(x+y(x))*(1-diff(y(x),x))^3; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= -x \\ \frac {x}{2}-\frac {4 \ln \left (27 y+27 x +8\right )}{27}+\frac {4 \ln \left (9 \left (x +y\right )^{{2}/{3}}-6 \left (x +y\right )^{{1}/{3}}+4\right )}{27}+\frac {4 \ln \left (2+3 \left (x +y\right )^{{1}/{3}}\right )}{27}-\frac {y}{2}-\frac {\left (x +y\right )^{{2}/{3}}}{2}-c_1 &= 0 \\ \frac {x}{2}-\frac {y}{2}-\frac {i \sqrt {3}\, \left (x +y\right )^{{2}/{3}}}{4}+\frac {\left (x +y\right )^{{2}/{3}}}{4}-c_1 &= 0 \\ \frac {x}{2}-\frac {y}{2}+\frac {i \sqrt {3}\, \left (x +y\right )^{{2}/{3}}}{4}+\frac {\left (x +y\right )^{{2}/{3}}}{4}-c_1 &= 0 \\ \end{align*}

✓ Mathematica. Time used: 178.922 (sec). Leaf size: 58354

ode=8*(1+D[y[x],x])^3==27*(x+y[x])*(1-D[y[x],x])^3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Too large to display

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-(1 - Derivative(y(x), x))**3*(27*x + 27*y(x)) + 8*(Derivative(y(x), x) + 1)**3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out