20.1.23 problem Problem 31

Internal problem ID [3580]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.2, Basic Ideas and Terminology. page 21
Problem number : Problem 31
Date solved : Sunday, March 30, 2025 at 01:51:48 AM
CAS classification : [`y=_G(x,y')`]

\begin{align*} y^{\prime }&=\frac {x^{2} \left (1-y^{2}\right )+y \,{\mathrm e}^{\frac {y}{x}}}{x \left ({\mathrm e}^{\frac {y}{x}}+2 x^{2} y\right )} \end{align*}

✓ Maple. Time used: 0.009 (sec). Leaf size: 21

ode:=diff(y(x),x) = (x^2*(1-y(x)^2)+y(x)*exp(y(x)/x))/x/(exp(y(x)/x)+2*x^2*y(x)); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.339 (sec). Leaf size: 24

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

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

✗ Sympy

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

Timed Out