83.10.7 problem 7

Internal problem ID [21976]
Book : Differential Equations By Kaj L. Nielsen. Second edition 1966. Barnes and nobel. 66-28306
Section : Chapter IV. First order differential equations of higher degree. Ex. XI at page 69
Problem number : 7
Date solved : Thursday, October 02, 2025 at 08:20:59 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

\begin{align*} y^{2}-2 x y y^{\prime }+{y^{\prime }}^{2} x^{2}-{y^{\prime }}^{3}&=0 \end{align*}

✓ Maple. Time used: 0.029 (sec). Leaf size: 35

ode:=y(x)^2-2*x*y(x)*diff(y(x),x)+x^2*diff(y(x),x)^2-diff(y(x),x)^3 = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 169.203 (sec). Leaf size: 27486

ode=y[x]^2-2*x*y[x]*D[y[x],x]+ D[y[x],x]^2*x^2- D[y[x],x]^3==0; 
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**2*Derivative(y(x), x)**2 - 2*x*y(x)*Derivative(y(x), x) + y(x)**2 - Derivative(y(x), x)**3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out