29.36.2 problem 1065

Internal problem ID [5629]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 36
Problem number : 1065
Date solved : Tuesday, March 04, 2025 at 10:48:00 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: 0.275 (sec). Leaf size: 80

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

✓ Mathematica. Time used: 69.994 (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