85.25.3 problem 3

Internal problem ID [22588]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. B Exercises at page 57
Problem number : 3
Date solved : Thursday, October 02, 2025 at 08:53:40 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational]

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

✓ Maple. Time used: 0.046 (sec). Leaf size: 31

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

\[ y = {\mathrm e}^{\operatorname {RootOf}\left ({\mathrm e}^{2 \textit {\_Z}}-2 \,{\mathrm e}^{\textit {\_Z}} x -\ln \left ({\mathrm e}^{\textit {\_Z}}-2 x \right )+c_1 +\textit {\_Z} \right )}-x \]

✓ Mathematica. Time used: 0.125 (sec). Leaf size: 39

ode=(x^3-x*y[x]^2+y[x])+(y[x]^3-x^2*y[x]-x)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\frac {1}{2} \left (-x^2-\log (y(x)-x)+\log (y(x)+x)\right )+\frac {y(x)^2}{2}=c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**3 - x*y(x)**2 + (-x**2*y(x) - x + y(x)**3)*Derivative(y(x), x) + y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out