88.7.10 problem 10

Internal problem ID [24005]
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 41
Problem number : 10
Date solved : Thursday, October 02, 2025 at 09:53:40 PM
CAS classification : [_exact, _rational]

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

✓ Maple. Time used: 0.009 (sec). Leaf size: 28

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

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

✓ Mathematica. Time used: 0.191 (sec). Leaf size: 24

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

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

✗ Sympy

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

Timed Out