32.6.48 problem Exercise 12.48, page 103

Internal problem ID [5913]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 12, Miscellaneous Methods
Problem number : Exercise 12.48, page 103
Date solved : Sunday, March 30, 2025 at 10:27:05 AM
CAS classification : [_rational]

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

✓ Maple. Time used: 0.021 (sec). Leaf size: 29

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

\[ y = {\mathrm e}^{\operatorname {RootOf}\left (-{\mathrm e}^{3 \textit {\_Z}}-\ln \left (x \right ) {\mathrm e}^{\textit {\_Z}}+c_1 \,{\mathrm e}^{\textit {\_Z}}-\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+x \right )} \]

✓ Mathematica. Time used: 0.255 (sec). Leaf size: 23

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

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

✗ Sympy

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

Timed Out