88.8.8 problem 8

Internal problem ID [24016]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 2. Differential equations of first order. Exercise at page 44
Problem number : 8
Date solved : Thursday, October 02, 2025 at 09:54:13 PM
CAS classification : [_rational]

\begin{align*} 2 x +2 x y^{2}-y^{3}-y^{5}+\left (1-3 x y^{2}-3 x y^{4}\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.008 (sec). Leaf size: 22

ode:=2*x+2*x*y(x)^2-y(x)^3-y(x)^5+(1-3*x*y(x)^2-3*x*y(x)^4)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\tan \left (\operatorname {RootOf}\left (-\textit {\_Z} +x \tan \left (\textit {\_Z} \right )^{3}+x^{2}+c_1 \right )\right ) \]

✓ Mathematica. Time used: 0.121 (sec). Leaf size: 23

ode=( 2*x+2*x*y[x]^2-y[x]^3-y[x]^5 )+( 1-3*x*y[x]^2-3*x*y[x]^4 )*D[y[x],{x,1}]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [-\arctan (y(x))-x^2+x y(x)^3=c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x*y(x)**2 + 2*x + (-3*x*y(x)**4 - 3*x*y(x)**2 + 1)*Derivative(y(x), x) - y(x)**5 - y(x)**3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out