89.32.12 problem 14

Internal problem ID [24972]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 16. Equations of order one and higher degree. Miscellaneous Exercises at page 246
Problem number : 14
Date solved : Thursday, October 02, 2025 at 11:45:12 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

\begin{align*} x^{2} {y^{\prime }}^{3}-2 x y {y^{\prime }}^{2}+y^{2} y^{\prime }+1&=0 \end{align*}

✓ Maple. Time used: 0.088 (sec). Leaf size: 82

ode:=x^2*diff(y(x),x)^3-2*x*y(x)*diff(y(x),x)^2+y(x)^2*diff(y(x),x)+1 = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 37.065 (sec). Leaf size: 33909

ode=x^2*D[y[x],x]^3-2*x*y[x]*D[y[x],x]^2+y[x]^2*D[y[x],x]+1==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)**3 - 2*x*y(x)*Derivative(y(x), x)**2 + y(x)**2*Derivative(y(x), x) + 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out