72.8.31 problem 31

Internal problem ID [19515]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Miscellaneous Problems for Chapter 2. Problems at page 99
Problem number : 31
Date solved : Thursday, October 02, 2025 at 04:35:52 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 11

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

\[ y = {\mathrm e}^{-\frac {c_1}{x^{3}}} \]

✓ Mathematica. Time used: 0.111 (sec). Leaf size: 20

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

\begin{align*} y(x)&\to e^{\frac {e^{c_1}}{x^3}}\\ y(x)&\to 1 \end{align*}

✓ Sympy. Time used: 0.239 (sec). Leaf size: 8

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

\[ y{\left (x \right )} = e^{\frac {C_{1}}{x^{3}}} \]