87.5.24 problem 39

Internal problem ID [23317]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 1. Elementary methods. First order differential equations. Exercise at page 47
Problem number : 39
Date solved : Thursday, October 02, 2025 at 09:31:51 PM
CAS classification : [_rational]

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

✓ Maple. Time used: 0.008 (sec). Leaf size: 23

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

\[ -2 x -\frac {\ln \left (x^{2}+y^{2}\right )}{2}-y+c_1 = 0 \]

✓ Mathematica. Time used: 0.118 (sec). Leaf size: 25

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

\[ \text {Solve}\left [\frac {1}{2} \log \left (x^2+y(x)^2\right )+y(x)+2 x=c_1,y(x)\right ] \]

✗ Sympy

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

Timed Out