81.15.16 problem 19-17

Internal problem ID [21724]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 19. Change of variables. Page 483
Problem number : 19-17
Date solved : Sunday, October 12, 2025 at 05:51:33 AM
CAS classification : [_rational]

\begin{align*} \frac {x^{2}}{y}+y^{2}-\left (\frac {x^{3}}{y^{2}}+x y+y^{2}\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.199 (sec). Leaf size: 38

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

\[ -\ln \left (y^{3}+x^{2}+2 x y+2 y^{2}\right )+\frac {x}{y}+2 \ln \left (y\right )+c_1 = 0 \]

✗ Mathematica

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

NotImplementedError : The given ODE -(x**2 + y(x)**3)*y(x)/(x**3 + x*y(x)**3 + y(x)**4) + Derivative(y(x), x) cannot be solved by the factorable group method