89.9.11 problem 11

Internal problem ID [24491]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 4. Additional topics on equations of first order and first degree. Exercises at page 72
Problem number : 11
Date solved : Thursday, October 02, 2025 at 10:42:33 PM
CAS classification : [_rational]

\begin{align*} 3 x^{2}+3 y^{2}+x \left (x^{2}+3 y^{2}+6 y\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.011 (sec). Leaf size: 21

ode:=3*x^2+3*y(x)^2+x*(x^2+3*y(x)^2+6*y(x))*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ c_1 +\frac {{\mathrm e}^{y} x \left (x^{2}+3 y^{2}\right )}{3} = 0 \]

✓ Mathematica. Time used: 0.092 (sec). Leaf size: 26

ode=3*( x^2+y[x]^2  )+x*( x^2+3*y[x]^2 +6*y[x]  )*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [x^3 e^{y(x)}+3 x e^{y(x)} y(x)^2=c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*x**2 + x*(x**2 + 3*y(x)**2 + 6*y(x))*Derivative(y(x), x) + 3*y(x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out