85.24.8 problem 8

Internal problem ID [22585]
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. A Exercises at page 57
Problem number : 8
Date solved : Thursday, October 02, 2025 at 08:53:34 PM
CAS classification : [_rational]

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

✓ Maple. Time used: 0.007 (sec). Leaf size: 21

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

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

✓ Mathematica. Time used: 0.13 (sec). Leaf size: 25

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

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

✗ Sympy

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

Timed Out