62.16.9 problem Ex 9

Internal problem ID [12829]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter IV, differential equations of the first order and higher degree than the first. Article 27. Clairaut equation. Page 56
Problem number : Ex 9
Date solved : Monday, March 31, 2025 at 07:19:03 AM
CAS classification : [`y=_G(x,y')`]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

Timed Out