85.24.6 problem 6

Internal problem ID [22583]
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 : 6
Date solved : Thursday, October 02, 2025 at 08:53:30 PM
CAS classification : [_rational]

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

✓ Maple. Time used: 0.018 (sec). Leaf size: 26

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

\[ y = x \cot \left (\operatorname {RootOf}\left (\tan \left (\textit {\_Z} \right ) c_1 -\textit {\_Z} \tan \left (\textit {\_Z} \right )-\tan \left (\textit {\_Z} \right ) x -x \right )\right ) \]

✓ Mathematica. Time used: 0.076 (sec). Leaf size: 17

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

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

✗ Sympy

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

Timed Out