16.9 problem Ex 9

Internal problem ID [11224]

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.
ODE order: 1.
ODE degree: 2.

CAS Maple gives this as type [`y=_G(x,y')`]

\[ \boxed {\left (x -y^{\prime }-y\right )^{2}-x^{2} \left (2 y x -x^{2} y^{\prime }\right )=0} \]

✗ Solution by Maple

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

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.0 (sec). Leaf size: 0

DSolve[(x-y'[x]-y[x])^2==x^2*(2*x*y[x]-x^2*y'[x]),y[x],x,IncludeSingularSolutions -> True]
                                                                                    
                                                                                    
 

Not solved