84.5.12 problem 3.4 (a)

Internal problem ID [22099]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 3. Classification of first-order differential equations. Solved problems. Page 11
Problem number : 3.4 (a)
Date solved : Thursday, October 02, 2025 at 08:24:49 PM
CAS classification : [[_homogeneous, `class G`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.015 (sec). Leaf size: 35

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

\begin{align*} y &= -x^{3}-\sqrt {x^{6}+c_1} \\ y &= -x^{3}+\sqrt {x^{6}+c_1} \\ \end{align*}

✓ Mathematica. Time used: 0.081 (sec). Leaf size: 48

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

\begin{align*} y(x)&\to -x^3-\sqrt {x^6+c_1}\\ y(x)&\to -x^3+\sqrt {x^6+c_1}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.158 (sec). Leaf size: 12

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

\[ \left [ y{\left (x \right )} = C_{1} - 3 \log {\left (x \right )}, \ y{\left (x \right )} = 0\right ] \]