87.5.10 problem 10

Internal problem ID [23303]
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 : 10
Date solved : Thursday, October 02, 2025 at 09:29:19 PM
CAS classification : [[_homogeneous, `class G`], _exact, _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Maple. Time used: 0.014 (sec). Leaf size: 53

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

\begin{align*} y &= \frac {-x^{3}+\sqrt {x \left (x^{5}+4 c_1 \right )}}{2 x} \\ y &= \frac {-x^{3}-\sqrt {x \left (x^{5}+4 c_1 \right )}}{2 x} \\ \end{align*}

✓ Mathematica. Time used: 0.306 (sec). Leaf size: 59

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

\begin{align*} y(x)&\to -\frac {x^3+\sqrt {x^6+4 c_1 x}}{2 x}\\ y(x)&\to \frac {-x^3+\sqrt {x^6+4 c_1 x}}{2 x} \end{align*}

✓ Sympy. Time used: 5.877 (sec). Leaf size: 39

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

\[ \left [ y{\left (x \right )} = \frac {x^{2} \left (\sqrt {\frac {C_{1}}{x^{5}} + 1} - 1\right )}{2}, \ y{\left (x \right )} = - \frac {x^{2} \left (\sqrt {\frac {C_{1}}{x^{5}} + 1} + 1\right )}{2}\right ] \]