88.5.4 problem 4

Internal problem ID [23978]
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 35
Problem number : 4
Date solved : Thursday, October 02, 2025 at 09:48:29 PM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Maple. Time used: 0.268 (sec). Leaf size: 31

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

\[ y = \frac {\operatorname {RootOf}\left (c_1 \,\textit {\_Z}^{8}-2 c_1 \,\textit {\_Z}^{2}-3 x^{2}\right )^{6}-2}{3 x} \]

✓ Mathematica. Time used: 60.172 (sec). Leaf size: 1499

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

\begin{align*} \text {Solution too large to show}\end{align*}

✗ Sympy

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

Timed Out