89.4.11 problem 12

Internal problem ID [24333]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 2. Equations of the first order and first degree. Exercises at page 39
Problem number : 12
Date solved : Thursday, October 02, 2025 at 10:18:30 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: 0.042 (sec). Leaf size: 26

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);
 

\[ y = x \cot \left (\operatorname {RootOf}\left (2 c_1 \sin \left (\textit {\_Z} \right )^{2}-2 \textit {\_Z} \sin \left (\textit {\_Z} \right )^{2}+x^{2}\right )\right ) \]

✓ Mathematica. Time used: 0.062 (sec). Leaf size: 31

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]
 

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

✗ 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